The Optics Laboratory
Group of Hans Hallen, Physics Department, North Carolina State University

Surface Enhancement in Near-Field Raman Spectroscopy

The NSOM is a good tool for studying surface enhancement, since the probe can be moved toward and away from the surface with very high precision. Force feedback can be used to stabilize the position if the probe is close enough to the surface. We expect that Raman spectra, and most other optical signals, will be enhanced as the NSOM probe approaches the surface, since there are many evanescent modes of the electric field near the tip than can begin to interact with the sample.

A good starting point is the Bethe-Bouwkamp model for electric fields near an aperture. To calculate the distance dependence, we use this model to calculate the electric field above the surface, then average the relevant quantity for all points in each plane above the surface, giving us one averaged value per distance,

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Independent calculation of the components is meaningful, since the vibration is usually along a bond, and only one component of the field will couple to the bond when the bond happens to line up with that axis. The squares of the projected fields appear in the Raman intensity, so they are shown. The calculation assumes light polarized along the x-direction incident on an aperture in the xy-plane. The plot with the derivative of Ez is what is expected in gradient field Raman, for comparison.

Below is a nano-Raman spectrum taken with our cooled CCD apparatus.

We take spectra similar to this at several distances from the surface, and subtract those taken closer from the average of several taken with the probe retracted from the surface – in the far-field. The difference spectra below represent the change as the probe enters the near field.

The spectra are shifted by 20 counts between each, and the spectra closer to the surface are towards the top of the figure. There are enhancements as one approaches the surface. At first one might think that these are simply enhancements of the existing Raman lines. They are not, since they are at different energies. Nor are they shifted by the same amount from the existing lines. They are at the energies of vibrations in KTP that are different than the vibrations observed in the far-field spectra. Two questions arise:

 Why aren’t the far-field Raman peaks enhanced? The top figure shows enhancement in all the electric fields, including X and Y, which are responsible for far-field Raman.

 Where do these new peaks come from?

The answer to the latter question is gradient field Raman, GFR, described on an accompanying web page. The answer to the former has to do with coupling of light from the tip region to the spectrometer. A theoretical map of the field profile shows the field in the x-direction (symmetric, large magnitude), and y-direction (4-fold symmetric, small magnitude) concentrated under the aperture:

  ,

while the z-component of the electric field is concentrated under the metal region around the aperture

 .

Combine this with the constraint that only perpendicular electric fields (light) are allowed near a metal surface,

,

to realize that the x- and y-polarized light cannot get around the probe tip to propagate to the spectrometer in reflection mode. These modes are enhanced, but their light is not detected in our experiment. The signal from the x and y modes that we do see probably originates from deeper within the sample.

To quantify the enhancement of the new peaks, we integrate the area under the peaks in the difference spectra, and subtract the background, as measured from averages on either side of the peaks. We obtain the following plots for the two main peaks in the difference spectra:

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The first change of the difference spectra from zero (the curves should continue to the right at zero), is a decrease at ~120 nm, before being enhanced at smaller z. This continues until the tip makes contact with the sample for the last two points. When contact is made, the vibration energies are modified by the stress of the probe tip, and the spectra change. We will ignore these data points in the following analysis. The two peaks, once scaled, are enhanced in almost exactly the same manner. This is because they are due to the same mechanism – GFR. A comparison with the predictions from the figure at the top of the page,

,

support this conclusion. The standard Raman mechanism predicts an Ez^2 dependence, which is too low at small z and too high at large z. The GFR derivative prediction does a good job with the qualitative trends, but misses the decrease at ~120 nm and increase ~70-90 nm. The origins of these oscillations are under investigation.

A truly near-field plasmon effect.

Several factors influence nano-Raman spectroscopy. Most result directly or indirectly from the metal that is used to localize the light so that nanoscale resolution can be attained. The metal quenches any electric field near a conducting surface that is not polarized perpendicular to the surface. This forces a strong gradient in the electric field component perpendicular to the metal surface in light propagation near a small metal object, since propagating light must be transverse away from the metal. The transition from normal to transverse polarization occurs in a scale of tens of nanometers, resulting in a very strong field gradient. This gradient allows a coupling between the optical field and a vibration known as gradient-field Raman (GFR) spectroscopy and provides the dominant contribution to the observed functional dependence of spectral peak amplitude versus probe sample distance noted above and below in the figures. This coupling acts in addition to the normal Raman coupling but has different selection rules, which favor bonds perpendicular to the metal surface with strong infrared coupling and largely complement normal Raman. Propagation of fields near the tip, in the figure below, also limit available optical interactions. The measured data above (especially the 'big peak' and 'little peak' plot) also show a drop to nearly zero as the tip is within a few nanometers of the sample. This results from the same physical mechanism as modification of fluorescence lifetime measurements with NSOM, the evanescent fields near the metal surface. These can have a larger momentum than propagating fields, so can by used to create electron-hole pairs in the metal -- these quickly sweep energy from the fields and result in the loss of a Raman signal. At larger distances, plasmons become important. While propagating fields in air cannot couple to a plasmon on a metal surface (again due to insufficient momentum for the energy so both can't be conserved), the evanescent fields near the tip (metal) can, or you can think of it as a coupling from within the tip, as photons in glass can have sufficient momentum to do so.

a.Fig Tip Pol b.Fig Model Geom c.Fig z-comp d.Fig x-comp

Figure 1. (a) A schematic drawing of an NSOM probe tip, illustrating a typical metal thickness (black) surrounding the tip of the etched silica fiber. Arrows indicate the polarization of light at various points. The ‘X’ emphasizes the boundary condition for electric field at a metal surface. (b) A schematic of the model geometry defines the dielectric constants, z-coordinate, and angle from the dipole emitting Raman shifted light, double arrow, to the outer edge of the tip, where interacts with the metal and scatters to the detector. (c,d) Images of the calculated squared electric field components for x-polarized light input into the probe. The sizes of the images are 3 apertures in both x and y, centered a distance 0.1 apertures below the tip of the probe. (c) The z-component, with range 0.07 a.u, (d) The x-component, with range 0.16 a.u.

To build a model for the near-field or tip-enhanced Raman process (TERS) with as few parameters as possible, we need to make a few assumptions and use some of the properties discussed. First, for reflection collection, the light needs to be z-polarized to make its way around the tip, so assume that. Second, the maximum excitation in the z-polarization is just under the edge of the aperture, so we assume the Raman emitting dipole is there. Third, the angle dependence of plasmon excitation will use depend upon θ, the arctangent of the coating thickness divided by the tip-sample distance. Interestingly, the standard plasmon derivation in terms of both transverse polarizations cannot describe the plasmonic feature observed (it can only produce a slight inflection). Thus, we must assume the plasmon is excited by the light polarized in the direction of propagation, one of the evanescent fields, which is much stronger than the propagating fields in this near-field region, so perhaps not too surprising. Its use produces the 'full model' curve in the figure below.

Fig Raman Comparison

Figure 2. The measured nano-Raman signal, dots with dotted line, is compared to a model that incorporates field gradient effects but not plasmons, dashed line, and the same model augmented to include plasmon generation, solid line. Both models have an arbitrary scale factor applied.

The minimum is now explained, but not the rise at smaller distances. This can be explained by allowing one bounce before the interference at the probe corner (and subsequent scattering to produce propagating light to be collected in the far field). The 'full model' is given by the form RamanModel = C|(ε2q2 - ε3q3)/(ε2q2 + ε3q3) + 1| × exp(imag(q2)z) cosθ Integral{ Ez(dEz/dz) dxdy}, with the ε's the dielectric constants of the layers as shown in the figure below, C a constant, and for each layer, q = 2π/λ sqrt(ε - ε2sin2θ). For the two bounce model, the |(ε2q2 - ε3q3)/(ε2q2 + ε3q3) + 1| is replaced by |(ε2q2 - ε3q3)/(ε2q2 + ε3q3) × (ε2q2 - ε1q1)/(ε2q2 + ε1q1) × exp(-2.3i × 2πzsqrt(ε2/λ)) + 1|. The result is a peak up into part of the region of increase in the plasmon effected area, but not all of it. As the dipole is located at different points under the aperture rim, the angle to a particular edge point varies. Thus, the angles change over a range, and this range will fill the range of distances that show an increase. The no-bounce case will also be present, giving the sharp dip. In other words, the entire curve is described by the model. We thus complete our qualitative and quantitative understanding of near-field Raman, also known as TERS. The key components are (1) field gradients, (2) propagation, (3) illumination field in the region of interest, (4) surface plasmons and other loss to the metal, and (5) dominance of the non-propagating fields.

a.Fig tip bounce b.Fig Raman Distance

Figure 3. Two models for the nano-Raman signal are considered. (a) A schematic drawing shows the single bounce case and the two bounce case. The former yields a model with one less parameter than the second. (b) The measured nano-Raman signal, dots, is compared to the two models. Both incorporate field gradient effects, include plasmon generation and near-field radial-polarization reflection coefficients, and have an arbitrary scale factor applied. The difference is a second reflection and more path length for the two-bounce case.

Nano-Raman spectra differ from far-field Raman spectra. The differences result from a strong electric field gradient near the metal tip, propagation, and polarization, but the dependence upon probe-sample distance can only be explained by the inclusion of surface plasmons and the near-field, non-propagating terms of the dipole emission. A simple model based upon these components accurately describes distance-dependent data measured with a near- field scanning optical microscope. Our essentially near-field model will apply generally to Raman spectroscopy near a nanoscale conductor.

  •  More info is in the papers.

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