Evanescent Wave

Definition

An evanescent wave is an electromagnetic field that does not propagate as a traveling wave, but rather exponentially decays in a direction perpendicular to the surface at which the wave is formed. This phenomenon is closely related to the concepts of total internal reflection and quantum tunneling.

5 Must Know Facts For Your Next Test

1. Evanescent waves are formed when light or other electromagnetic waves are totally internally reflected at a surface, such as the interface between two media with different refractive indices.
2. The intensity of an evanescent wave decreases exponentially with the distance from the reflecting surface, with the decay length typically on the order of the wavelength of the light.
3. Evanescent waves can be used to probe the properties of materials near the surface, as they only interact with a small region beyond the reflecting surface.
4. In the context of quantum tunneling, evanescent waves describe the exponential decay of the wavefunction of a particle as it penetrates a potential energy barrier that it does not have enough energy to classically overcome.
5. Evanescent waves play a crucial role in various applications, such as near-field optical microscopy, surface plasmon resonance sensors, and the operation of certain types of waveguides and optical devices.

Review Questions

• Explain how evanescent waves are formed and their relationship to total internal reflection.
  • Evanescent waves are formed when light or other electromagnetic waves are totally internally reflected at the interface between two media with different refractive indices. When the angle of incidence in the first medium is greater than the critical angle, the wave is completely reflected back into the first medium, but an evanescent wave is generated at the interface. This evanescent wave does not propagate as a traveling wave, but rather exponentially decays in the direction perpendicular to the surface. The formation of evanescent waves is a direct consequence of the total internal reflection phenomenon.
• Describe the role of evanescent waves in the context of quantum tunneling and explain how they relate to the exponential decay of the wavefunction.
  • In the context of quantum tunneling, evanescent waves describe the exponential decay of the wavefunction of a particle as it penetrates a potential energy barrier that it does not have enough energy to classically overcome. When a particle encounters a potential energy barrier, its wavefunction does not abruptly terminate at the barrier, but rather extends into the barrier region as an evanescent wave. This evanescent wavefunction decays exponentially within the barrier, with the decay length determined by the height and width of the barrier. The exponential decay of the evanescent wavefunction is a key feature of quantum tunneling, as it allows the particle to have a non-zero probability of being found on the other side of the barrier, even though it does not have enough energy to classically surmount the barrier.
• Discuss the various applications of evanescent waves and how their unique properties are leveraged in these applications.
  • Evanescent waves have a wide range of applications due to their unique properties. In near-field optical microscopy, evanescent waves are used to probe the properties of materials near the surface, as they only interact with a small region beyond the reflecting surface. Surface plasmon resonance sensors utilize the sensitivity of evanescent waves to changes in the refractive index near the surface to detect the presence of specific molecules or interactions. Additionally, evanescent waves play a crucial role in the operation of certain types of waveguides and optical devices, where they are used to confine and manipulate light at the nanoscale. The exponential decay of evanescent waves also makes them useful in applications such as the design of optical filters and the development of high-resolution imaging techniques. Overall, the unique characteristics of evanescent waves, such as their localized nature and exponential decay, make them a valuable tool in various fields of science and technology.

Related terms

Total Internal Reflection:

The total reflection of a wave at the interface between two media when the angle of incidence in the first medium is greater than the critical angle, causing the wave to be reflected back into the first medium.

Quantum Tunneling:

The quantum mechanical phenomenon where a particle can penetrate and pass through a potential energy barrier despite not having enough energy to classically overcome the barrier.

Exponential Decay:

The process by which a quantity decreases at a rate proportional to its current value, following an exponential function.