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raman spectroscopy is a powerful technique which has become one of the optical workhorses in analytical chemistry where it is used to detect and quantify a variety of chemical substances including biomolecules absorbed to a substrate .
the 1974 report by fleischmann _
et al . _
@xcite on surface - enhanced raman spectroscopy ( sers ) created an avalanche in surface - enhanced spectroscopies  @xcite .
localized surface plasmons may dramatically enhance the otherwise intrinsically weak raman scattering [ see panel ( a ) in fig .
[ fig1 ] ] and this has paved the way for chemical detection in very dilute solutions , reaching the limit of single - molecule detection  @xcite .
initially , there was a strong emphasis on disordered and rough metal surfaces  @xcite ; however during the past decade the use of highly engineered surface plasmonic structures has been envisioned  @xcite .
the latter development has to a large extent been fueled by the rapid development of a variety of nanofabrication technologies , including high - resolution electron - beam lithography on the true nano scale . as a consequence ,
surface plasmon subwavelength optics has in general developed tremendously  @xcite , and in particular sers has been observed for a large variety of nanostructures , such as nanorods , nanorings , triangular nanoprisms , nanocubes , nanocrescents , and nanorice  @xcite .
field localization is the key to understanding and further enhancing sers .
structures with pronounced bends in their surface @xmath2 will tend to localize the field also in the plane of the surface  @xcite .
singular points , such as sharp kinks and corners , may lead to nonanalytic or even mathematically divergent electric fields .
real structures are smooth , of course , at least on some microscopic length scale .
all fabrication processes have their inherent upper bounds on the sharpness that can be fabricated reproducibly . as an example
, state - of - the - art groove waveguides have sharp features down to a 10  nm scale  @xcite . in an ensemble of nanostructures
there will always be a size dispersion or structure - to - structure fluctuations in some details of the geometry , for example the nanoscale rounding @xmath3  @xcite will differ from structure to structure , with possibly far - reaching effects on the sers .
fluctuations between repeated features and variations in the smoothness of individual features have previously been addressed for fractal structures in a number of papers by snchez - gil _ et al .
_ , see e.g. refs .
the pronounced sample - to - sample fluctuations are potentially a serious challenge to the development of a technology for reliable use in quantitative sensing applications and bio - chemical analysis .    in this paper
we address another crucial issue : how are the high enhancement factors found for highly ideal surface structures affected by round - off effects ?
by means of numerical examples we shall illustrate the extreme precision needed in the fabrication of nanostructured surfaces , if one aims at sers in the excess of ten orders of magnitude .
specifically , we consider the simple model geometry in panel ( b ) of fig .  [ fig1 ] .
historically , this was the first structure considered theoretically to explain the large enhancement occurring for rough metal surfaces  @xcite . today , we may easily envision realization of groove structures  @xcite closely resembling the geometry considered in panel ( c ) , though state - of - the - art structures may still be somewhat larger in scale . as mentioned above
, the points of intersection of neighboring cylinders may lead to a singularity in the electric field , and consequently arbitrarily large enhancement factors [ see eq .
( [ eq : gamma ] ) below ] .
in the context of sers it is customary to estimate the surface - enhancement factor @xmath4 from  @xcite @xmath5 where @xmath6 is the position of the molecule . to a first approximation
the surface - enhancement factor is independent on the intrinsic properties of the molecule . here ,
@xmath2 is the surface bounding the volume @xmath7 occupied by metal , @xmath8 is the incident field , and the total field is @xmath9 with @xmath10 being the scattered component that arises in the presence of the metal surface .
the surface - averaged enhancement factor applies to the case of a spatially uniform surface - coverage of molecules .
our theoretical study takes the wave equation for the electrical field as a starting point @xmath11 where @xmath12 is the angular frequency and @xmath13 is the vacuum velocity of light . for structures as in fig .
[ fig1 ] the spatially dependent relative dielectric function is of the form @xmath14 where @xmath15 is the dielectric function of the metal . to make our simulations mimic a real material we use the bulk dielectric constant of silver ( thus neglecting spatial dispersion near the metal surface ) , illustrated in fig .
[ fig2 ] which shows standard handbook data for @xmath15  @xcite along with a numerical fit to the drude expression @xmath16 with @xmath17 being the plasma frequency and @xmath18 the damping rate .
this simple model accounts very well for the real part , however some deviations are seen in the visible for the imaginary part .
the spectral position of resonances will thus be accurately predicted by using the drude fit while we shall see that even small deviations in the imaginary part of @xmath19 may influence the enhancement factor , eq .
( [ eq : gamma ] ) , by orders of magnitude .
in the following we use a finite - element approach ( comsol multiphysics ) to solve eq .
( [ eq : wave ] ) in a unit cell resembling panel ( c ) in fig
.  [ fig1 ] .
we apply periodic boundary conditions in the direction parallel to the surface .
deep inside the metal and far out in the free space we employ perfectly - matched layers in the perpendicular direction  @xcite , so that the domain has an extension @xmath20 , i.e. significantly exceeding the free - space wavelength .
( [ eq : wave ] ) is solved for a normal incident electrical field polarized perpendicular to the groove axis , see panel ( b ) in fig .
[ fig1 ] , which strongly polarizes the surface by excitation of a surface - plasmon resonance . with the resulting scattered field , and hence @xmath21
, we subsequently evaluate eq .
( [ eq : gamma ] ) by a boundary integration routine .
our meshing is chosen to ensure convergence of the enhancement factor ; this requires a particularly fine mesh in the groove region . as an example , resolving the peak in @xmath4 at resonance has typically required a sub - nanometer meshing . on a standard - equipped pc
the calculation of a single near - resonance frequency point typically takes around 30 seconds .
figure  [ fig3 ] shows the wavelength dependence of the surface - averaged enhancement factor in the case of @xmath22  nm and @xmath23  nm .
the solid line shows results based on the drude model , eq .
( [ eq : drude ] ) , while the points are obtained from a simulation using the discrete frequencies where handbook data is available , see fig .
first , we note that these geometrical parameters easily lead to surface - averaged enhancement factors in excess of @xmath24 , i.e. twelve orders of magnitude , in the visible .
second , when inspecting the peak around @xmath25  nm and comparing the two simulations , it is also clear that the drude model , eq .
( [ eq : drude ] ) , overestimates the enhancement by perhaps up to three orders of magnitude .
this overestimation may be traced back to the imaginary part of @xmath19 shown in fig .
[ fig2 ] where the drude model seriously underestimates the broadening of the surface - plasmon resonance . finally , when approaching the ultra - violet , resonances predicted by the drude model are barely visible when employing the handbook data directly .
while general trends can be extracted from a drude description , these results emphasize the need for an accurate material - dispersion law for even semi - quantitative predictions of sers .
in particular , the surface - plasmon damping is crucial in the vicinity of resonances as clearly seen in the dashed traces where we for illustrative purposes have increased the damping rate @xmath18 by a factor of two , five , and ten .    while previous studies  @xcite have reported a spectrally broadened enhancement , our detailed finite - element simulations suggest the existence of highly peaked enhancement factors associated with the formation of a surface - plasmon resonance strongly localized in the groove .
a related transverse localization has recently been reported experimentally for groove waveguides  @xcite and subsequently confirmed numerically  @xcite . obviously , spatial localization is the route to high enhancement and especially one should minimize the overlap with the lossy metal causing ohmic broadening of resonances .
the nanoscale cutoff @xmath3 is the geometrical knob that controls the strength of localization and the overlap with the metal . a stronger localization ( @xmath26 )
will usually be expected to squeeze up the resonance in frequency space . however , when increasing @xmath3 we actually observe a blue - shift which can be understood within the quasi - static framework of ref .
@xcite [ see their eq .
( 4 ) ] where an increase in metal volume @xmath7 causes modes at @xmath12 to blue - shift to a frequency @xmath27 with a less negative dielectric function , i.e. @xmath28 . in fig .
[ fig4 ] we illustrate this point for varying values of @xmath3 at fixed @xmath22  nm . for simplicity
the results are based on the drude model .
our results show that even for a relatively conservative value of the ratio @xmath29 the enhancement has already dropped to @xmath30 compared to @xmath31 in the case of @xmath32 .
another geometric factor affecting the field enhancement is the radius of cylinders . in fig .
[ fig5 ] we illustrate this point for varying values of @xmath33 at fixed @xmath34  nm , again using the drude model .
our results show a red - shift of the resonance when increasing the radius while the magnitude decreases slightly .
the red - shift may be understood qualitatively from the scale invariance of eq .
( [ eq : wave ] ) in the absence of material dispersion
[ fig4 ]  and  [ fig5 ] together illustrate how the enhancement is influenced by both length scales @xmath33 and @xmath3 in a nontrivial interplay .
in conclusion , we have presented finite - element simulations of the sers enhancement factor for an example of a nanostructured surface , which represents the state - of - the - art technology .
we find that a well - defined structure , with mathematically sharp boundaries [ see eq .
( [ eq : eps ] ) ] , may exhibit huge enhancement factors , @xmath35 .
but any geometric smoothening rapidly decreases the enhancement , and even though a computational optimization may be possible by a painstaking survey of the parameter space ( _ given _ that the dielectric function of the material is known very accurately - no small feat by itself ! ) , it is doubtful whether the extremely high theoretical enhancement factors can be reached in practice and in a reproducible manner .
we acknowledge stimulating discussions with s.  i. bozhevolnyi . this work is financially supported by the _ danish council for strategic research _ through the _ strategic program for young researchers _ ( grant no : 2117 - 05 - 0037 ) and the _ danish research council for technology and production sciences _ ( grant no : 274 - 07 - 0379 ) as well as the fidipro program of the finnish academy .
k.  kneipp , y.  wang , h.  kneipp , l.  t. perelman , i.  itzkan , r.  dasari , and m.  s. feld , `` single molecule detection using surface - enhanced raman scattering ( sers ) '' , phys .
* 78 * 1667  1670 ( 1997 ) .
j. jung , t. sndergaard , and s.  i. bozhevolnyi , `` theoretical analysis of square surface plasmon - polariton waveguides for long - range polarization - independent waveguiding '' , phys .
b * 76 * 035434 ( 2007 ) .
j.  a. snchez - gil , j.  v. garca - ramos , and e.  r. mndez , `` near - field electromagnetic wave scattering from random self - affine fractal metal surfaces : spectral dependence of local field enhancements and their statistics in connection with surface - enhanced raman scattering '' , phys .
b * 62 * 10515  10525 ( 2000 )
.    j.  a. snchez - gil , j.  v. garca - ramos , and e.  r. mndez , `` electromagnetic mechanism in surface - enhanced raman scattering from gaussian - correlated randomly rough metal substrates '' , opt .
express * 10 * 879  886 ( 2002 )
.    s.  i. bozhevolnyi , v.  s. volkov , e.  devaux , j.  y. laluet , and t.  w. ebbesen , `` channel plasmon subwavelength waveguide components including interferometers and ring resonators '' , nature * 440 * 508  511 ( 2006 ) .
surface - enhanced raman spectroscopy ( sers ) allows single - molecule detection due to the strong field localization occurring at sharp bends or kinks of the metal - vacuum interface . 
 an important question concerns the limits of the signal enhancement that can be achieved via a judicious design of the surface . by using a specific example of a technologically realizable nanopatterned surface , 
 we demonstrate that while very high enhancement factors ( @xmath0 can be found for an ideal surface , these are unlikely to be achieved in laboratory samples , because even a minute , inevitable rounding - off strongly suppresses the enhancement , as well as shifts the optimal frequency . 
 our simulations indicate that the geometric enhancement factors are unlikely to exceed @xmath1 for real samples , and that it is necessary to consider the geometric uncertainty to reliably predict the frequency for maximum enhancement .