photonic nanojets - northwestern engineering · this paper reviews the substantial body of...

REVIEW

Copyright copy 2009 American Scientific PublishersAll rights reservedPrinted in the United States of America

Journal ofComputational and Theoretical Nanoscience

Vol 6 1979ndash1992 2009

Photonic Nanojets

Alexander Heifetz1 dagger Soon-Cheol Kong2lowast dagger Alan V Sahakian12Allen Taflove2 and Vadim Backman1

1Department of Biomedical Engineering 2Department of Electrical Engineering and Computer ScienceNorthwestern University Evanston IL 60208 USA

This paper reviews the substantial body of literature emerging since 2004 concerning photonic nano-jets The photonic nanojet is a narrow high-intensity non-evanescent light beam that can propagateover a distance longer than the wavelength after emerging from the shadow-side surface of anilluminated lossless dielectric microcylinder or microsphere of diameter larger than The nano-jetrsquos minimum beamwidth can be smaller than the classical diffraction limit in fact as small as sim3for microspheres It is a nonresonant phenomenon appearing for a wide range of diameters of themicrocylinder or microsphere if the refractive index contrast relative to the background is less thanabout 21 Importantly inserting within a nanojet a nanoparticle of diameter d perturbs the far-fieldbackscattered power of the illuminated microsphere by an amount that varies as d3

for a fixed Thisperturbation is much slower than the d6

dependence of Rayleigh scattering for the same nanopar-ticle if isolated This leads to a situation where for example the measured far-field backscatteredpower of a 3-m diameter microsphere could double if a 30-nm diameter nanoparticle were insertedinto the nanojet emerging from the microsphere despite the nanoparticle having only 110000ththe cross-section area of the microsphere In effect the nanojet serves to project the presence ofthe nanoparticle to the far field These properties combine to afford potentially important applica-tions of photonic nanojets for detecting and manipulating nanoscale objects subdiffraction-resolutionnanopatterning and nanolithography low-loss waveguiding and ultrahigh-density optical storage

Keywords Scattering Mie Theory FDTD

CONTENTS

1 Introduction 19792 Initial Identification of the Photonic Nanojet for a

Dielectric Cylinder 19813 Initial Identification of the Photonic Nanojet for a

Dielectric Sphere 19824 Photonic Nanojet Theory 19845 Laboratory Observations 19866 Potential Applications 1987

61 Low-Loss Optical Waveguiding 198762 Enhanced Raman Scattering 198963 Two-Photon Fluorescence Enhancement 198964 Maskless Subwavelength-Resolution Direct-Write

Nanopatterning 199065 Nanoparticle Detection Sizing and Location 199066 Directional Emission in a Symmetrical Aggregate of

Spherical Particles 199067 Inspection of Semiconductor Wafers 199168 Optical Trapping of Metal Nanoparticles 199169 Ultrahigh-Density Optical Data-Storage Disks 1991

7 Summary and Conclusions 1991Acknowledgments 1992References 1992

lowastAuthor to whom correspondence should be addresseddaggerCo-principal author

1 INTRODUCTION

Since 2004 a substantial literature1minus20 has developedregarding the existence properties and potential appli-cations of the photonic nanojet The photonic nanojetis a narrow high-intensity electromagnetic beam thatpropagates into the background medium from the shadow-side surface of a plane-wave illuminated lossless dielec-tric microcylinder or microsphere of diameter greater thanthe illuminating wavelength Key properties of the pho-tonic nanojet include (1) It is a non-evanescent propa-gating beam that can maintain a subwavelength full-widthat half-maximum (FWHM) transverse beamwidth along apath that can extend more than sim2 beyond the dielectriccylinder or sphere (2) Its minimum FWHM beamwidthcan be smaller than the classical diffraction limit in factas small as sim3 for microspheres (3) It is a nonreso-nant phenomenon that can appear for a wide range of thediameter d of the dielectric microcylinder or microspherefrom sim2 to more than 40 if the refractive index contrastrelative to the background medium is less than about 21

J Comput Theor Nanosci 2009 Vol 6 No 9 1546-1955200961979014 doi101166jctn20091254 1979

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Photonic Nanojets Heifetz et al

(4) It has a high intensity that can significantly exceed thatof the illuminating wave (5) Inserting within a nanojet ananoparticle of diameter d perturbs the far-field backscat-tered power of the illuminated microsphere by an amountthat varies as d3

for a fixed This perturbation is muchslower than the d6

dependence of Rayleigh scattering forthe same nanoparticle if isolated This leads to a situationwhere for example the measured far-field backscatteredpower of a 3-m diameter microsphere could double if a

Alexander Heifetz received BS (Suma Cum Laude) in 1999 in Applied Math MS in2002 in Physics and PhD in 2005 in Electrical Engineering (Optics) all from Northwest-ern University in Evanston IL He was a recipient of Walter P Murphy Graduate Fellowshipat Northwestern University His doctoral thesis work was on diffraction of light from holo-graphic gratings for data storage and image correlation applications Alexander is currentlyan American Cancer SocietyCanary Foundation postdoctoral fellow in the Biomedical Engi-neering Department at Northwestern University His research interests are in electromagneticscattering theory and simulations for biomedical applications His most recent publicationsare on light scattering from nanoparticles and biological cells using Mie theory and theFDTD method

Soon-Cheol Kong received the BS MS and PhD degrees from Chung-Ang UniversitySeoul Korea in 1995 1997 and 2003 respectively From 2002 to 2006 he was a SeniorResearcher with the SAMSUNG Electro-Mechanics Suwon Korea and was a Visiting Scien-tist with MIT from 2004 to 2005 Currently he works as a post doctoral fellow at NorthwesternUniversity His research interests include FDTD method microwave-photonics micronanoelectromagnetics biophotonics for applications of antennas traveling-wave photodetectosultrahigh-density optical storage solar cells bio-detection and early-stage cancer detection

Alan V Sahakian received the PhD in ECE with a minor in CS and the MSEE fromthe University of WisconsinndashMadison During his graduate study he was also a SeniorElectrical Engineer at Medtronic Inc His BS was in Applied Science and in Physics fromthe University of Wisconsin-Parkside He is currently Professor of EECS and BME and theAssociate Chair of EECS for the undergraduate program at Northwestern University He isalso the Director of the EECS Signals and Systems Division and a member of the academicaffiliate staff at Evanston Hospital He has served as a resident visiting scholar in the Centerfor Excellence in Reliability and Maintainability at the Air Force Institute of Technology Heis a Fellow of the IEEE In addition to cardiac electrophysiology his lab studies microwavemillimeter wave and photonic methods of medical imaging and diagnostics His researchis funded by the NSF the Department of Defense Breast Cancer Research Program theDefense Intelligence Agency the Dr Scholl Foundation and Medtronic Inc

Allen Taflove is a professor of electrical engineering and computer science at NorthwesternUniversity Evanston Illinois USA He has helped to pioneer finite-difference time-domain(FDTD) algorithms and applications since 1971 His publications include more than125 journal papers and three editions (1995 2000 and 2005) of the book ComputationalElectrodynamics The Finite-Difference Time-Domain Method which has become a standardreference in the FDTD field He is listed by the Institute for Scientific Information as oneof the most cited technical authors in the world

30-nm diameter nanoparticle were inserted into the nanojetemerging from the microsphere despite the nanoparticlehaving only 110000th the cross-section area of the micro-sphere In effect the nanojet serves to project the presenceof the nanoparticle to the far fieldThese properties combine to afford potentially impor-

tant applications of photonic nanojets for detectingand manipulating nanoscale objects subdiffraction-resolution nanopatterning and nanolithography low-loss

1980 J Comput Theor Nanosci 6 1979ndash1992 2009

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Heifetz et al Photonic Nanojets

Vadim Backman is a Professor of Biomedical Engineering at McCormick School ofEngineering and Applied Sciences Northwestern University He received a PhD inMedical Engineering from Harvard University and Massachusetts Institute of Technol-ogy Dr Backman received numerous awards including being selected as one of the top100 young innovators in the world by Technology Review Magazine and the NationalScience Foundation CAREER award Dr Backmanrsquos research interests include developmentof novel biophotonics technologies for non-invasive screening diagnosis and detection ofdisease The focus is on the nanoscale the microscale and the molecular levels

waveguiding and ultrahigh-density optical storage Withthe aim of encouraging nanojet research this paper sum-marizes progress in the nanojet area to-date Discussionsinclude the initial identification of the photonic nanojet fora dielectric cylinder (Section 2) the initial identificationof the photonic nanojet for a dielectric sphere (Section 3)photonic nanojet theory (Section 4) laboratory observa-tions (Section 5) and potential applications (Section 6)

2 INITIAL IDENTIFICATION OF THEPHOTONIC NANOJET FORA DIELECTRIC CYLINDER

The initial identification of the photonic nanojet as a dis-tinct electromagnetic wave type and the coining of thedescriptor ldquophotonic nanojetrdquo was reported by Chen et al1

Applying a high-resolution finite-difference time-domain(FDTD) computational solution of Maxwellrsquos equations21

evidence was provided that a plane-wave illuminatedmicron-scale circular dielectric cylinder can generatea narrow high-intensity subdiffraction-waist beam thatpropagates into the background medium from the cylin-derrsquos shadow-side surface Furthermore it was reportedthat positioning a nanometer-scale dielectric cylinderwithin the nanojet causes a giant perturbation of thebackscattered power of the micron-scale dielectric cylinderemitting the nanojet That is the perturbation is orders ofmagnitude larger than the backscattering of the nanoscalecylinder when considered in isolationReference [1] first reviewed the validation of its FDTD

computational technique which employed a uniformsquare cell size of 125 nm (finer than 1100th dielec-tric wavelength for all modeling runs) and the perfectlymatched layer absorbing outer grid boundary condition21

Upon comparing the FDTD-computed differential scat-tering cross-section of several homogeneous isotropiccircular dielectric cylinders with the exact series solu-tion agreement was found to within plusmn1 dB over theentire range of scattering angles for all cases studied overdynamic ranges of 60 dBReference [1] then reported detailed two-dimensional

computational studies of the internal and near-externalfields of a series of homogeneous isotropic losslessinfinitely long circular dielectric cylinders Each cylinder

was assumed to be illuminated by a plane wave polarizedwith the incident electric field parallel to the cylinderrsquosinfinite axis Figure 1 shows sample results illustrating theevolution of a photonic nanojet as the refractive index ofa circular dielectric cylinder decreases Here the FDTD-computed envelope of the sinusoidal steady-state electricfield is visualized for a d = 5 m diameter circular cylin-der of uniform refractive index n1 embedded within aninfinite vacuum medium of refractive index n2 = 10 Lightof wavelength 2 = 500 nm propagates from left to rightin medium 2 Upon decreasing n1 from 35 in Figure 1(a)to 25 in Figure 1(b) the internal electric-field peak shiftstoward the shadow-side surface of the cylinder Upon fur-ther decreasing n1 to 17 in Figure 1(c) the electric-fieldpeak emerges from the shadow-side surface of the cylinderas a strong jet-like distribution having a length of sim900 nm(182) and a weakly subdiffraction FWHM intensity waistof sim200 nm (042) The emergence of this jet from theshadow-side surface of the cylinder for n1 sim 2 is consistentwith previous work on optical caustics2223

Reference [1] then reported that weakly subdiffraction-waist photonic nanojets similar to that in Figure 1(c)can be generated using a variety of combinations of dn1 n2 and 2 provided that n1n2 is not significantlychanged from that of Figure 1(c) Examples are illus-trated in Figure 2 for (a) d = 5 m n1 = 35 n2 =20 2 = 250 nm (b) d = 6 m n1 = 23275 n2 =133 2 = 300 nm and (c) d = 10 m n1 = 23275n2 = 133 2 = 300 nm Including the case of Figure 1(c)the FWHM intensity waists of all nanojets modeled rangedbetween 042 and 0482 and the lengths of all nanojetsmodeled ranged between 162 and 22Finally using FDTD modeling Ref [1] considered the

impact of positioning a nanometer-scale perturbing dielec-tric cylinder within the nanojet generated by a micron-scale primary cylinder The test case used the parametersof Figure 2(b) ie a 6 m diameter primary circularcylinder of refractive index n1 = 23275 embedded withinan infinite exterior medium of refractive index n2 = 133and illuminated at the wavelength 2 = 300 nm The per-turbing dielectric nanocylinder was assumed to have asquare cross-section of side dimension d = 5 nm andrefractive index n = 15 This nanocylinder was insertedin the FDTD model at the center of the photonic nanojeton the surface of the 6 m diameter primary cylinder

J Comput Theor Nanosci 6 1979ndash1992 2009 1981

Delivered by Ingenta toUniversitaet Duisburg-Essen

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Fig 1 Visualizations of the evolution of a photonic nanojet as the refractive index of a plane-wave-illuminated circular dielectric cylinder decreasesThe FDTD-computed envelope of the sinusoidal steady-state electric field is visualized for a d= 5 m diameter cylinder of uniform refractive index n1

embedded within an infinite vacuum medium of refractive index n2 = 10 Light of wavelength 2 = 500 nm propagates from left to right in medium 2(a) n1 = 35 (b) n1 = 25 (c) n1 = 17 Reprinted with permission from [1] Z G Chen et al Opt Express 12 1214 (2004) copy 2004 Optical Societyof America

Figure 3(a) graphs the absolute value of the result-ing perturbation of the differential scattering cross-sectionof the primary microcylinder within plusmn10 of backscatterThis figure also graphs the corresponding differential scat-tering cross-section of the isolated plane-wave illuminatedperturbing nanocylinder These results show that the per-turbation of the direct backscattering cross-section of themicrocylinder provided by the 5-nm dielectric nanocylin-der located within the nanojet is approximately 45times104-times greater than the backscattering of the isolatednanocylinder Figure 3(b) illustrates the results of addi-tional FDTD modeling studies in Ref [1] which show thatthis effective enhancement of the backscattering of the per-turbing nanocylinder designated as E increases monoton-ically as d decreases below 20 nm reaching a level ofapproximately 106 for d = 125 nm

As a result of these computational modeling studiesit was concluded in Ref [1] that photonic nanojets mayprovide a new means to detect nanoparticles of size wellbelow the classical diffraction limit This could potentiallyyield means to use visible light to detect proteins viral par-ticles and even single molecules and to monitor molec-ular synthesis and aggregation processes of importance inmany areas of biology chemistry materials sciences andtissue engineering

3 INITIAL IDENTIFICATION OF THEPHOTONIC NANOJET FORA DIELECTRIC SPHERE

The initial identification of the photonic nanojet for adielectric sphere was reported by Li et al2 Their approach



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Fig 2 Visualizations of the generation of photonic nanojets similar to that in Figure 1(c) for three different combinations of d n1 n2 and 2(a) d = 5 m n1 = 35 n2 = 20 2 = 250 nm (b) d = 6 m n1 = 23275 n2 = 133 2 = 300 nm (c) d = 10 m n1 = 23275 n2 = 1332 = 300 nm Reprinted with permission from [1] Z G Chen et al Opt Express 12 1214 (2004) copy 2004 Optical Society of America

involved implementing an exact eigenfunction series solu-tion of Maxwellrsquos equations in spherical coordinates (ieMie theory) to compute the near field external to eachplane-wave illuminated dielectric sphere of interest In thismanner evidence was provided that a plane-wave illumi-nated micron-scale dielectric sphere can generate a fullythree-dimensional photonic nanojet having a weakly sub-diffraction minimum beamwidth This nanojet has prop-erties that are similar to its two-dimensional counterpartproduced by a plane-wave illuminated circular dielectriccylinder of comparable size and refractive index contrastrelative to the background medium However the nano-jet generated by the dielectric sphere has an even higherintensity than the nanojet generated by the dielectric cylin-der Furthermore the backscattered power of the dielectricsphere is perturbed to an even greater degree than that ofthe dielectric cylinder when a nanometer-scale particle ispositioned within the nanojet

Referring to Figure 4 Ref [2] first studied a series ofhomogeneous isotropic dielectric microspheres of refrac-tive index n= 159 Each microsphere was assumed to beilluminated in an infinite vacuum region by an x-polarizedz-propagating plane wave with unit intensity and wave-length = 400 nm Figures 4(a) (b) (c) and (d) visualizethe computed near-external field of each microsphere fordiameters d = 1 m 2 m 35 m and 8 m respec-tively For d less than 4 m (Figs 4(andashc)) a weaklysubdiffraction-waist nanojet protrudes from the shadowside of the sphere For larger d (Fig 4(d)) the intensitypeak of the nanojet moves away from the microspherersquossurface Also noted is that both the maximum intensity andFWHM waist of the nanojet increase as d increases

Reference [2] then studied the magnitude of the per-turbation of the backscattered power of the d = 35 mmicrosphere of Figure 4(c) caused by the passage ofa d = 20 nm gold nanoparticle of refractive index


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(a)

(b)

Fig 3 (a) FDTD-calculated absolute value of the perturbation of thedifferential scattering cross-section of the circular (primary) dielectriccylinder for the case of Figure 2(b) (d = 6 m n1 = 23275 n2 = 1332 = 300 nm) The perturbation is caused by placing a 5-nm squaredielectric nanocylinder (n = 15) on the surface of the primary micro-cylinder at the center of the photonic nanojet (b) Effective backscatteringenhancement factor E versus side dimension of the perturbing nanocylin-der Reprinted with permission from [1] Z G Chen et al Opt Express12 1214 (2004) copy 2004 Optical Society of America

n = 147minus j195 through the nanojet generated by micro-sphere We shall designate the peak backscattered powerperturbation magnitude caused by the gold nanoparticle as Figure 5(a) which shows all particle dimensions to-scale illustrates how the gold nanoparticle was assumedto travel in the y-direction along a straight-line path inthe vacuum located 240 nm from the shadow-side sur-face of the primary microsphere The backscattering ofthe composite microspheregold nanoparticle system wascomputed using the generalized multiparticle Mie (GMM)technique which provides a rigorous analytical solutionfor electromagnetic wave scattering by multiple spheresbased upon the addition theorems for vector sphericalwave functions2425

Referring to Figure 5(b) it was determined that thed = 20 nm gold nanoparticle moving along the path illus-trated in Figure 5(a) causes a peak backscattered powerperturbation = 40 relative to the backscattered powerof the isolated microsphere This is a relatively giant per-turbation only 4 dB below the full backscattered power ofthe isolated microsphere that is caused by a nanoparticlefully 175-times smaller than the microsphere in diameter(ie more than 30000-times smaller than the microspherein cross-section area)Referring to Figure 5(c) the above study was repeated

for gold nanoparticles ranging in diameter from d = 2 nmto d = 60 nm It was determined that increases mono-tonically over this size range in fact exceeding 100 ofthe backscattered power of the isolated microsphere forgold nanoparticles as small as d = 27 nm (sim1130th ofthe diameter of the microsphere) Interestingly a d =2 nm gold particle ie a clump of about 100 gold atomswas found to generate a just 34 dB below the fullbackscattered power of the isolated microsphere Conse-quently instruments having a dynamic range of 40 dBor more could detect such near atomic-level size particlesusing visible lightFurthermore Figure 5(c) reveals that the backscattered

power perturbation caused by the gold nanoparti-cle increases as d3

over the nanoparticle diameter range2 nm le d le 20 nm (ie 200 le d le 20) Thisis a much slower than the d6

dependence of RayleighscatteringReference [2] proceeded to calculate for each gold

nanoparticle diameter the effective backscattering enhance-ment factor E provided by the photonic nanojet E wasdefined as normalized by the backscattered powerof the isolated plane-wave illuminated gold nanoparticleReferring to Figure 6(a) it was determined that E risesfrom approximately 3times 104 to 2times 108 as the size of thegold nanoparticle drops from 60 nm to 2 nm These val-ues are respectively 30-times larger and 200-times largerthan the corresponding enhancement factors for the two-dimensional cylinder nanojet case shown in Figure 3(b)For nanoparticle diameters below 20 nm this increase inE takes on a dminus3

dependence In combination with theappreciable values of in this size range (Fig 5(c)) itbecomes possible to distinguish between gold nanoparti-cles having diameters differing by as little as 1 nm asshown in Figure 6(b)

4 PHOTONIC NANOJET THEORY

Lecler et al3 applied Mie theory to analyze the generalthree-dimensional vectorial properties of photonic nano-jets generated by plane-wave illuminated dielectric micro-spheres in free space They reported that nanojets can begenerated for a wide range of microsphere diameters d

from sim2 to greater than 40 They further reported that



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Fig 4 Visualizations of the photonic nanojets generated by illuminating dielectric microspheres of refractive index n = 159 in vacuum with a= 400 nm x-polarized z-propagating plane waves of unit intensity The near fields are computed using the Mie series (a) d = 1 m microspherediameter (b) d = 2 m (c) d = 35 m (d) d = 8 m Reprinted with permission from [2] X Li et al Opt Express 13 526 (2005) copy 2005Optical Society of America

the sub-wavelength waist of the nanojet is a consequenceof the proximity of the microspherersquos shadow-side surfaceand its focus point in the exterior region (with the micro-sphere considered as a lens) Specifically for the micro-spheres considered it was found that the nanojet waistremains sub-wavelength for a maximum propagation dis-tance of sim2 for an optimum microsphere refractive indexn sim 13 Finally nanojets were shown to have the sameelectric-field polarization as the incident plane wave butwith an asymmetric beamwidth (narrower in the directionof the incident magnetic field)Itagi and Challener4 provided a detailed analysis of the

optics of photonic nanojets in two dimensions for thecase of a plane-wave illuminated infinitely long dielec-tric cylinder Their starting point was an eigenfunctionsolution of the Helmholtz equation which was recastinto a Debye series (an infinite sum of inward and out-ward radially propagating cylindrical wave modes eachof which can undergo reflection and transmission at thecylinder surface) It was shown that the first term of theDebye series is of particular importance This term yieldsa compact expression which connects the physical and

geometrical optics properties of the nanojet and permitsa straightforward field analysis Overall nanojet charac-teristics were concluded to arise from a ldquounique combi-nation of featuresrdquo in the angular spectrum involving thephase distribution and the finite content of propagating andevanescent spatial frequenciesChen et al5 reported a perturbation analysis based upon

GMM theory for the microspherenanoparticle system toexamine the mathematical origins of the sim d3

andE sim dminus3

variations calculated in Ref [2] It was stated thatthe lens focusing effect of the incident illumination by thedielectric microsphere can account for at most three of themaximum eight orders of magnitude of the backscatter-ing enhancement factor E shown in Figure 6(a) Further-more because the lens focusing effect is constant over thed range considered it contributes nothing to the calcu-lated variations of and E with d The physical ori-gins of the sim d3

and E sim dminus3 variations remained

unexplainedDevilez et al20 studied the spatial and spectral

properties of the three-dimensional photonic nanojet in aframework employing rigorous Lorentz-Mie theory They


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Fig 5 (a) Passage of a d = 20 nm diameter gold nanoparticle through the nanojet of Figure 4(c) (b) Resulting 40 perturbation of thebackscattered power of the 35-m diameter dielectric microsphere (c) Backscattered power perturbation in dB relative to the backscattered powerof the isolated 35-m diameter dielectric microsphere of (a) Reprinted with permission from [2] X Li et al Opt Express 13 526 (2005) copy 2005Optical Society of America

quantitatively evaluated the contributions from all spatialfrequency components both propagating and evanescentWhile their study indicated predominantly propagating-wave contributions to the nanojet the evanescent field con-tributions created by the illuminated microsphere enhanceand sharpen the nanojetrsquos field distribution A key con-clusion of this analysis was that the angular openings ofphotonic nanojets are at least twice as small as those incomparable Gaussian beams

5 LABORATORY OBSERVATIONS

Heifetz et al6 reported an experimental confirmation ofthe photonic jet for a dielectric sphere and its associatedgiant backscattering perturbation phenomenon previouslypredicted in Refs [1] and [2] To facilitate the measure-ments the originally reported diameter of the dielectricsphere was scaled upward from the micron scale illumi-nated by visible light to the centimeter scale illuminated by


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(a)

(b)

Fig 6 (a) Effective backscattering enhancement factor E of the per-turbing gold nanoparticle versus its diameter d (b) Sensitivity of thebackscattered power of the microspheregold nanoparticle system tonanometer variations of the gold nanoparticle diameter d from 18 to22 nm Reprinted with permission from [2] X Li et al Opt Express13 526 (2005) copy 2005 Optical Society of America

microwaves at 30 GHz (= 1 cm) Specifically the dielec-tric sphere had a diameter of 762 cm (762) and wascomprised of an acrylic material (polymethylmethacrylate)having the refractive index n = 160+ j00016

Figure 7(a) depicts the measured data of Ref [6] forthe backscattering perturbation caused by a d = 1 mm(10) metal particle scanned along the central propaga-tion axis of the microwave jet Here z is the distancebetween the shadow-side surface of the acrylic sphere andthe surface of the metal particle There is good agree-ment between the measured and FDTD-computed datasetswhich show that oscillates between positive and nega-tive values depending upon z The perturbation is ldquogiantrdquoin the sense that the 1-mm metal particle nearly doublesthe backscattered power of the acrylic sphere if located atz = 2 mm 10 mm and 15 mm and nearly cuts in halfthe backscattered power of the acrylic sphere if located atz= 6 mm 12 mm and 18 mm This is despite the 1-mm

metal particle having a diameter 76-times smaller than theacrylic sphere (ie an area almost 6000-times smaller)Figure 7(b) shows results analogous to Figure 7(a) but

for the 1-mm metal particle scanned laterally across themicrowave jet in the electric-field direction along a lineat z = 9 mm (09) from the shadow-side surface of theacrylic sphere There is again good agreement between themeasured and FDTD-computed datasetsFigure 8 depicts the measured data of Ref [6] for

the dependence of the backscattered power perturbation upon the diameter d of a perturbing metal parti-cle that is located on the central propagation axis of themicrowave jet at z = 9 mm (09) Here the slope ofthe straight-line fit to the measured data yields the depen-dence sim d334

over the range of metal particle diameters1 mmle d le 3 mm (equivalently 01le d le 03) Thisis consistent with the theoretical dependence graphed inFigure 5(b) obtained using the GMM technique for per-turbing nanoparticles with diameters d ge 40 nm (equiva-lently d ge 01 because of the = 400 nm illuminationwavelength assumed in Fig 5(b))Ferrand et al13 reported the direct experimental obser-

vation of photonic nanojets at an optical wavelength asillustrated in Figure 9 Here nanojets were generated bylatex microspheres (refractive index= 16) of 1 m 3 mand 5 m diameters deposited on a glass coverslip andilluminated by a plane wave at = 520 nm Measurementswere performed using a fast scanning confocal microscopein the detection mode Each fully three-dimensional pho-tonic nanojet was reconstructed from a collected stack ofimages which had been corrected by a numerical deconvo-lution procedure to account for the detection point spreadfunction of the system Measurements indicated nanojetbeamwidths as small as 270 nm FWHM for a 3-mdiameter microsphere with the nanojets maintaining sub- FWHM beamwidths over propagation distances of morethan 3

6 POTENTIAL APPLICATIONS

61 Low-Loss Optical Waveguiding

Astratov715 reported experimental observations of the for-mation and propagation of nanojet-induced modes (NIMs)in linear chains of several tens of touching polystyrenemicrospheres (refractive index n= 159) with mean diam-eters in the 2ndash10 m range At long distances from thesource measured propagation losses for NIMs were aslow as 008 dB per microsphere within a chain formed by5-m diameter microspheresOptical waveguiding in chains of microspheres via

NIMs may be advantageous relative to optical waveguid-ing via intersphere coupling of whispering gallery modessince NIMs are not resonant modes and are inherently



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(a)

(b)

Fig 7 (a) Measured and FDTD-calculated backscattering perturbation (dB) caused by a d = 1 mm (10) metal particle scanned along the centralpropagation axis of the 30-GHz (= 1 cm) microwave jet z is the distance between the shadow-side surface of the d = 762 cm (762) acrylic sphereand the surface of the metal particle (b) Same as (a) but for the 1-mm metal particle scanned laterally across the microwave jet in the electric-fielddirection along a line at z = 9 mm (09) from the shadow-side surface of the acrylic sphere Reprinted with permission from [6] A Heifetz et alAppl Phys Lett 89 221118 (2006) copy 2006 American Institute of Physics

Fig 8 Measured dependence of the backscattered power perturbation (dB) upon the diameter d of the perturbing metal particle that is located onthe central propagation axis of the 30-GHz (= 1 cm) microwave jet at the distance z= 9 mm (09) from the shadow-side surface of the d = 762 cm(762) acrylic sphere Reprinted with permission from [6] A Heifetz et al Appl Phys Lett 89 221118 (2006) copy 2006 American Institute of Physics



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Fig 9 (a) Visualization of the experimentally measured photonic nanojet generated by a 5 m latex microsphere (refractive index= 16) resting ona glass coverslip as viewed in a vertical plane cutting through the center of the microsphere The illumination is a downward-propagating plane waveat = 520 nm (b) Measured intensity normalized to a peak value of unity along a horizontal line cutting through the narrowest point of the nanojetRed dots measured data solid line Gaussian curve fit (c) Measured intensity normalized to that of the incident wave along a vertical line belowthe microsphere at the center of the nanojet Blue dots measured data solid line Lorenzian curve fit (d) FWHM beamwidth of the nanojet versusdistance below the microsphere Green dots measured data dashed line numerical simulation results for the microsphere assumed to be in free spaceReprinted with permission from [13] P Ferrand et al Opt Express 16 6930 (2008) copy 2008 Optical Society of America

broadband With NIMs variations of microsphere diam-eters within a long chain due to normal fabrication tol-erances have little or no impact upon the waveguidingcharacteristics

62 Enhanced Raman Scattering

Yi et al8 reported an experimental observation of enhancedRaman scattering by self-assembled silica microspheres(10 m diameter refractive index n = 15) They con-cluded that the presence of strongly localized opticalelectric fields within photonic nanojets associated withthe silica microspheres accounts for the enhanced RamanscatteringMicrosphere-enhanced Raman spectroscopy may be

advantageous relative to conventional surface-enhanced

Raman scattering (SERS) approaches because8 (1) thelocation and size of the dielectric microspheres can bewell controlled eliminating problems with reproducibil-ity in SERS (2) sample preparation is much simpler and(3) enhanced effects by microspheres can occur for mostRaman-active substrates such as silicon The technique haspotential applications in areas of surface science such asoxidation adhesion corrosion and catalytic processes

63 Two-Photon Fluorescence Enhancement

Lecler et al9 reported an experimental observation ofthe nonlinear enhancement of two-photon excited fluo-rescence from a molecular dye solution brought aboutby adding drops of a suspension of silica microspheres(059plusmn 01 m diameter refractive index n = 15) They


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argued that the nonlinear absorption is enhanced due tophotonic nanojets associated with the microspheres andsuggested that photonic jets could be used to enhance othernonlinear optical effects

64 Maskless Subwavelength-ResolutionDirect-Write Nanopatterning

Wu et al10 reported an experimental demonstration of amaskless subwavelength-resolution direct-write nanopat-terning technique which uses a self-assembled planar arrayof transparent silica or polystyrene microspheres (097 mdiameter) deposited on top of a photoresist in a singlelayer Upon a brief (08 s) illumination at = 400 nmthe photoresist was not exposed except at the locationsof the high-intensity photonic nanojets associated with themicrospheres Over a large photoresist area this yielded aregular 097 m period array of 250 nm diameter holes(or pillars if using negative resist processing) It was deter-mined that this technique provides accurate control of thehole or pillar diameter by varying the exposure time Inaddition the array period could be accurately and inde-pendently controlled by using different microsphere sizesFurthermore because the nanojet waist is only a weakfunction of the microsphere diameter an extremely uni-form array of hole or pillar sizes could be achieved evenfor relatively poor microsphere size uniformityMcLeod and Arnold16 reported the direct writing of

complex nanopatterns on a polyimide film substrate usingoptically trapped microspheres Here a = 532 nmcontinuous-wave laser generating a Bessel beam servedto optically trap and manipulate a polystyrene or silicamicrosphere The trapped microsphere was simultaneouslyilluminated with a = 355 nm pulsed Gaussian beam togenerate the nanojet which locally modified the substrateOptimal results were achieved using 076-m polystyrenemicrospheres In this manner arbitrary patterns and indi-vidual features with minimum sizes of sim100 nm (lessthan one-third of the writing wavelength) were demon-strated A positioning accuracy of better than 40 nm wasattained in aqueous and chemical environments and sub-micron spacing between the microsphere and the substratewas maintained without active feedback control

65 Nanoparticle Detection Sizing and Location

As reviewed in Section 3 using the GMM analytical tech-nique Ref [2] first reported the possibility of detectingand sizing gold nanospheres having diameters as smallas 2 nm by exploiting the giant backscattering perturba-tion phenomenon of the photonic nanojet generated bya dielectric microsphere Subsequently Ref [11] appliedthe GMM technique to determine that using the pho-tonic nanojet a 20-nm diameter gold nanosphere could belocated with a subdiffraction transverse spatial resolution

in the magnetic-field direction as fine as 3 in the back-gound medium when the nanosphere is approximately 4behind the dielectric microsphere that originates the nano-jet The backscattering perturbation signal that locates thegold nanoparticle is no more than one order of magnitudebelow the backscattering of the isolated microsphere eventhough the nanoparticle is only 1100th the diameter of themicrosphereIn combination Refs [2] and [11] indicate that it is

possible to use visible light to detect size and locatewith subdiffraction resolution nanoparticles as small as afew nanometers at standoff distances of appreciable frac-tions of the wavelength A potential biophotonics applica-tion involves the detection of nanoparticles attached to themembranes of living cells in an aqueous environment Ina conceptual experiment a cell could be scanned with thenanojet emanating from an optically trapped microspherewhich would have a soft-spring recoil and hence wouldminimize potential damage to the biological sample

66 Directional Emission in a Symmetrical Aggregateof Spherical Particles

Gerlach et al12 reported optical measurements of smallsymmetrical arrays of contacting latex microspheres(refractive index n= 168 diameter= 537plusmn007 m iesim16) Here strong optical coupling between the micro-spheres can result in a complex rearrangement of theirmode structure similar to the electronic molecular orbitalsin a chemical molecule This analogy motivated the usageof the term ldquophotonic moleculerdquo12

The following compact groupings were tested (a) threemicrospheres located at the vertices of an equilateral tri-angle (b) five microspheres located at the vertices ofan equilateral pentagon and (c) seven microspheres withsix located at the vertices of an equilateral hexagon sur-rounding a seventh microsphere located at the center Eachgrouping was formed on a silicon wafer substrate Uponillumination with a defocused laser beam perpendicular tothe silicon substrate (ie the molecule plane) photonicnanojets were observed propagating outward symmetri-cally from each of the microspheres located at the verticesof each grouping Nanojet emission was visible in the farfield due to reflection from the silicon substrateIt was concluded that the observed directed emission

of photonic nanojets enables possible uses of symmetri-cal groupings of microspheres as transverse beam split-ters having a number of output ports equal to the numberof microspheres located at the vertices of the equilat-eral triangle pentagon hexagon etc arrangement beingused Furthermore such beam splitting could allow trans-verse coupling from an impinging laser beam onto pho-tonic components such as waveguides laid out along aplanar substrate This coupling could be possible withsub-wavelength spatial accuracy and yield much higher


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intensities than conventional sub-wavelength couplingtechniques using scanning near-field optical microscopytips

67 Inspection of Semiconductor Wafers

Chen et al17 patented means to perform optical metrol-ogy of a semiconductor wafer using a photonic nanojet Inthis technique the inspection area of the wafer is scannedwith a nanojet and measurements are obtained of theretroreflected light from the dielectric microsphere used togenerate the nanojet The presence type and dimensionsof a wafer-surface feature are determined by comparingthe backscattered light signature with a library of suchsignatures for both desired structures and contaminatingparticles

68 Optical Trapping of Metal Nanoparticles

Cui et al18 theoretically investigated the optical forcesacting on a metal nanoparticle located within a photonicnanojet generated by a plane-wave illuminated dielec-tric microcylinder It was found that these optical forcesdepend strongly on the dielectric permittivity of thenanoparticle and the intensity and beamwidth of the nano-jet While subwavelength metal nanoparticles can be effi-ciently trapped within a nanojet the attractive force can bechanged to a repulsive force simply by varying the polar-ization of the incident illumination This reversal is relatedto the nanoparticlersquos polarizability and excitation of local-ized surface plasmons Overall these findings are promis-ing for the application of photonic nanojets to ldquoprovidehighly confined force fields to efficiently organize nano-structures in the nanoscalerdquo18

69 Ultrahigh-Density Optical Data-Storage Disks

Kong et al1419 computationally and experimentally inves-tigated the potential application of the photonic nano-jet to implement ultrahigh-density optical data-storagedisks wherein data are encoded as nanoscale pits ina metal substrate This application is based upon thegiant backscattering perturbation phenomenon previouslyreported for isolated nanoparticles located within ananojet256 but here nanoscale pits in the disk substrate(rather than isolated nanoparticles) generate the backscat-tering perturbations As illustrated in Figure 10 microwavemeasurements on dimensionally scaled-up disk models andFDTD computational models indicate that pits having alateral area of 0025 square wavelengths ie much smallerthan current BluRaytrade device features can be robustlydetected with a contrast ratio approximately 28 dB greaterthan provided by a lens system1426 These findings sub-sequently extended to optical wavelengths19 using FDTDcomputational modeling suggest that photonic nanojetscould lead to the development of optical-disk data-storage

(a)

(b)

Fig 10 (a) Comparative experimental and FDTD data for the nanojet-induced no-pitndashto-pit power ratio versus wavelength for a rectangular pitof lateral dimensions 125 mm (08times 2 mm (05) and depth 2 mm(05) Both datasets show a peak no-pitndashto-pit power ratio that is approx-imately 700-times (ie 28 dB) greater than the 12 value reported inRef [25] using a conventional lens for an octagonal pit of approxi-mately the same lateral area in square wavelengths (b) Visualizationof the FDTD-computed microwave intensity distribution for the pit caseof (a) There is a strong nanojet intensity localization in the vicinity ofthe pit with a peak value of sim225 times the incident The backscat-tered wave intensity decreases with distance from the front surface of thesphere faster than for the no-pit case yielding a much weaker far-fieldbackscattered response Reprinted with permission from [14] S-C Konget al Appl Phys Lett 92 211102 (2008) copy 2008 American Instituteof Physics

technology having much greater capacity and speed thanthe present state of the art

7 SUMMARY AND CONCLUSIONS

This paper has reviewed the substantial body of literatureemerging since 2004 concerning photonic nanojets Dis-cussions included a review of the initial identificationof the photonic nanojet for the dielectric cylinder andsphere properties of the photonic nanojet nanojet theorylaboratory observations and potential applications Pho-tonic nanojets exhibit a unique combination of desirableattributes including wave propagation (rather than evanes-cence) along multiwavelength paths narrow potentiallysubdiffraction beamwidths high intensity little wave-length sensitivity and giant backscattering perturbations


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for nanoparticles and nanopits Consequently photonicnanojets hold considerable promise for advancing currentnanophotonic technologies ranging from ultramicroscopyto optical data storage to nanopatterning to biophotonics

Acknowledgments The photonic nanojet research byour group was supported in part by National Institutesof Health Grant R01 EB003682 and National ScienceFoundation Grants CBET-0939778 and CBET-0522639Alexander Heifetz PhD was supported by the CanaryFoundationAmerican Cancer Society Early DetectionPostdoctoral Fellowship Jim Spadaro and Nikola Borisovmanaged and maintained Professor Backmanrsquos computercluster

References

1 Z G Chen A Taflove and V Backman Opt Express 12 1214(2004)

2 X Li Z Chen A Taflove and V Backman Opt Express 13 526(2005)

3 S Lecler Y Takakura and P Meyrueis Optics Lett 30 2641(2005)

4 A V Itagi and W A Challener J Opt Soc America A 22 2847(2005)

5 Z G Chen X Li A Taflove and V Backman Optics Lett 31196 (2006)

6 A Heifetz K Huang A V Sahakian X Li A Taflove andV Backman Appl Phys Lett 89 221118 (2006)

7 A M Kapitonov and V N Astratov Optics Lett 32 409 (2007)

8 K J Yi H Wang Y F Lu and Z Y Yang J Applied Physics101 063528 (2007)

9 S Lecler S Haacke N Lecong O Creacutegut J-L Rehspringer andC Hirlimann Opt Express 15 4935 (2007)

10 W Wu A Katsnelson O G Memis and H MohseniNanotechnology 18 485302 (2007)

11 A Heifetz J J Simpson S-C Kong A Taflove and V BackmanOpt Express 15 17334 (2007)

12 M Gerlach Y P Rakovich and J F Donegan Opt Express 1517343 (2007)

13 P Ferrand J Wenger A Devilez M Pianta B Stout N BonodE Popov and H Rigneault Opt Express 16 6930 (2008)

14 S-C Kong A V Sahakian A Heifetz A Taflove andV Backman Appl Phys Lett 92 211102 (2008)

15 S Yang and V N Astratov Appl Phys Lett 92 261111 (2008)16 E McLeod and C B Arnold Nature Nanotech 3 413 (2008)17 Z Chen H Chu and S Li Optical metrology using a photonic

nanojet US Patent 7394535 (2008)18 X Cui D Erni and C Hafner Opt Express 16 13560 (2008)19 S-C Kong A Sahakian A Taflove and V Backman Opt Express

16 13713 (2008)20 A Devilez B Stout N Bonod and E Popov Opt Express 16

14200 (2008)21 A Taflove and S C Hagness Computational Electrodynamics The

Finite-Difference Time-Domain Method 3rd edn Artech Boston(2005)

22 C L Adler J A Lock B R Stone and C J Garcia J Opt SocAmerica A 14 1305 (1997)

23 J A Lock C L Adler and E A Hovenac J Opt Soc AmericaA 17 1846 (2000)

24 Y L Xu and R T Wang Phys Rev E 58 3931 (1998)25 Online httpwwwastroufledusimxu26 J A C Veerman A J H Wachters A M van der Lee and H P

Urbach Opt Express 15 2075 (2007)

Received 5 June 2008 Accepted 6 October 2008


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(4) It has a high intensity that can significantly exceed thatof the illuminating wave (5) Inserting within a nanojet ananoparticle of diameter d perturbs the far-field backscat-tered power of the illuminated microsphere by an amountthat varies as d3

for a fixed This perturbation is muchslower than the d6

dependence of Rayleigh scattering forthe same nanoparticle if isolated This leads to a situationwhere for example the measured far-field backscatteredpower of a 3-m diameter microsphere could double if a

Alexander Heifetz received BS (Suma Cum Laude) in 1999 in Applied Math MS in2002 in Physics and PhD in 2005 in Electrical Engineering (Optics) all from Northwest-ern University in Evanston IL He was a recipient of Walter P Murphy Graduate Fellowshipat Northwestern University His doctoral thesis work was on diffraction of light from holo-graphic gratings for data storage and image correlation applications Alexander is currentlyan American Cancer SocietyCanary Foundation postdoctoral fellow in the Biomedical Engi-neering Department at Northwestern University His research interests are in electromagneticscattering theory and simulations for biomedical applications His most recent publicationsare on light scattering from nanoparticles and biological cells using Mie theory and theFDTD method

Soon-Cheol Kong received the BS MS and PhD degrees from Chung-Ang UniversitySeoul Korea in 1995 1997 and 2003 respectively From 2002 to 2006 he was a SeniorResearcher with the SAMSUNG Electro-Mechanics Suwon Korea and was a Visiting Scien-tist with MIT from 2004 to 2005 Currently he works as a post doctoral fellow at NorthwesternUniversity His research interests include FDTD method microwave-photonics micronanoelectromagnetics biophotonics for applications of antennas traveling-wave photodetectosultrahigh-density optical storage solar cells bio-detection and early-stage cancer detection

Alan V Sahakian received the PhD in ECE with a minor in CS and the MSEE fromthe University of WisconsinndashMadison During his graduate study he was also a SeniorElectrical Engineer at Medtronic Inc His BS was in Applied Science and in Physics fromthe University of Wisconsin-Parkside He is currently Professor of EECS and BME and theAssociate Chair of EECS for the undergraduate program at Northwestern University He isalso the Director of the EECS Signals and Systems Division and a member of the academicaffiliate staff at Evanston Hospital He has served as a resident visiting scholar in the Centerfor Excellence in Reliability and Maintainability at the Air Force Institute of Technology Heis a Fellow of the IEEE In addition to cardiac electrophysiology his lab studies microwavemillimeter wave and photonic methods of medical imaging and diagnostics His researchis funded by the NSF the Department of Defense Breast Cancer Research Program theDefense Intelligence Agency the Dr Scholl Foundation and Medtronic Inc

Allen Taflove is a professor of electrical engineering and computer science at NorthwesternUniversity Evanston Illinois USA He has helped to pioneer finite-difference time-domain(FDTD) algorithms and applications since 1971 His publications include more than125 journal papers and three editions (1995 2000 and 2005) of the book ComputationalElectrodynamics The Finite-Difference Time-Domain Method which has become a standardreference in the FDTD field He is listed by the Institute for Scientific Information as oneof the most cited technical authors in the world

30-nm diameter nanoparticle were inserted into the nanojetemerging from the microsphere despite the nanoparticlehaving only 110000th the cross-section area of the micro-sphere In effect the nanojet serves to project the presenceof the nanoparticle to the far fieldThese properties combine to afford potentially impor-

tant applications of photonic nanojets for detectingand manipulating nanoscale objects subdiffraction-resolution nanopatterning and nanolithography low-loss


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photonic nanojets - northwestern engineering · this paper reviews the substantial body of...

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