Lecture 3- Nanophotonics

Evanescent Waves in Nanophotonics — Class Notes

Evanescent Waves in Nanophotonics

Conceptual + Physical + Application View (with analogy)

1. What is an Evanescent Wave?

An evanescent wave is a non-propagating electromagnetic field that appears at an interface and decays exponentially away from that interface.

Unlike ordinary (far-field) light that travels through space carrying energy, an evanescent wave:

  • does not travel forward in the direction of decay,
  • is localized near the surface,
  • stores energy rather than transporting it away.

2. Core Mathematical Picture

A normal propagating wave can be written as:

\(E(x,t)=E_0\,e^{i(kx-\omega t)}\)

Here \(k\) is real, so the field oscillates and energy propagates.

An evanescent field decays exponentially:

\(E(x)=E_0\,e^{-x/d_p}\)

\(d_p\) is the penetration depth (often around 50–100 nm for visible light). So the field becomes negligible within a fraction of a wavelength.

Imaginary wavevector idea: In the decay direction the wavevector becomes imaginary: \(k=i\kappa\). Then \(e^{ikx}\rightarrow e^{-\kappa x}\), changing oscillation into exponential decay.

3. Why Does This Happen? (Physical Insight)

Evanescent waves appear when propagation is not allowed. The second region behaves like a forbidden zone. The field cannot drop abruptly to zero at the boundary, so it “leaks” slightly into the forbidden region, but decays exponentially.

4. Forbidden Zone Analogy: Quantum Tunneling

Electron (Quantum Mechanics): If an electron meets a barrier higher than its energy, it cannot pass classically, but its wavefunction penetrates slightly into the barrier and decays:

\(\psi(x)\propto e^{-\kappa x}\)

Photon (Optics): Similarly, when light reaches a region where it cannot propagate (for example, the air side in total internal reflection), the electromagnetic field penetrates slightly and decays. That decaying field is the evanescent wave.

Same mathematics, different systems: tunneling of electrons ↔ evanescent decay of light.

5. How Are Evanescent Waves Created?

A. Total Internal Reflection (TIR)

When light travels in a high refractive index medium (glass) and hits a lower index medium (air) at an angle greater than the critical angle, it reflects back completely. But the field “leaks” slightly into the air and decays exponentially — this is the evanescent wave.

Simple picture: Like a ball thrown up a hill. It cannot cross, but it climbs a little before rolling back. That small “penetration” region is analogous to the evanescent field.

B. Sub-Wavelength Apertures (Near-Field Tip)

If light is forced through a hole smaller than its wavelength, it cannot propagate normally. Instead, a localized near-field forms at the aperture and decays quickly — an evanescent field. This is the principle behind Near-Field Scanning Optical Microscopy (NSOM).

6. Why Evanescent Waves Matter in Nanophotonics

Evanescent waves carry high spatial frequency information about features smaller than the wavelength of light. In ordinary microscopy, this information is lost because lenses mainly collect propagating (far-field) waves.

Diffraction limit: Conventional resolution is roughly \(\sim \lambda/2\) (about 200–300 nm for visible light).

To access sub-wavelength details (10–50 nm), we must interact with the evanescent field before it decays — by placing a probe/sample extremely close (near-field region).

7. Plasmonics (Surface-Confinement)

Surface plasmons are electromagnetic waves coupled to electron oscillations at a metal–dielectric interface. They propagate along the surface but are evanescent perpendicular to the surface. This produces strong confinement and field enhancement at nanoscale.

8. Superlenses and Metamaterials

In ordinary materials, evanescent waves decay. Some metamaterial “superlenses” are designed to amplify these evanescent components, restoring sub-wavelength information and enabling imaging beyond the diffraction limit.

9. Key Takeaways

  • Evanescent waves are non-propagating fields that decay exponentially away from an interface.
  • They occur when light encounters a forbidden propagation region (e.g., TIR, sub-wavelength apertures).
  • They carry the nano-scale (sub-wavelength) information that far-field optics cannot capture.
  • They are central to near-field microscopy, plasmonics, and superlensing.
Evanescent waves are the “hidden part” of light that dies near the surface — nanophotonics is the science of using it before it disappears.

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