A sharp metal tip (Au/Ag apex, radius a) held a gap d above a molecule on a mirror-like substrate concentrates the incident field into a nanoscale "gap-mode" hot spot — this is tip-enhanced Raman spectroscopy (TERS), the scanning-probe cousin of surface-enhanced Raman (SERS).
Treating the tip apex as a polarizable sphere of radius a, its induced near field falls off as a dipole field measured from the sphere's centre, distance r = a + d:
Local field ratio: g(d) = ( a / (a + d) )³
Image-dipole coupling to the substrate roughly doubles the exponent,
so the intensity (Raman scales as field&sup4;) enhancement factor is
EF(d, λ) ≈ g(d)⁴ × g(d)⁴ × L(λ) = ( a / (a+d) )¹² × L(λ)
L(λ) = 1 / (1 + ((λ − λres)/Γ)²) λres = 500 + 2a nm, Γ = 45 nm
The steep d−12-type decay is why TERS/SERS signal comes almost entirely from sub-nanometre "hot spots" — and why lateral spatial resolution beats the optical diffraction limit (∼λ/2, hundreds of nm). Resolution is set by the geometric mean of tip radius and gap:
Lateral resolution Δx ≈ 1.0 × √(a × d)
- Gap slider — shrinking d collapses the hot spot and spikes the enhancement factor by orders of magnitude.
- Tip radius slider — a sharper tip (smaller a) trades some peak enhancement for much better spatial resolution.
- Wavelength slider — the enhancement peaks when the laser matches the tip's localized plasmon resonance.
- Start Raster Scan — sweeps the tip across three fixed molecules on the sample; the strip below builds a real Raman intensity image line-by-line, revealing features narrower than the optical spot size.
Real-world relevance: this is the working principle behind commercial TERS microscopes, which image individual molecules and even resolve intramolecular vibrational modes with nanometre resolution — something impossible with a diffraction-limited laser spot alone.