What are Evanescent Waves?

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- GoPhotonics

Jun 12, 2023

Evanescent waves are electromagnetic waves that exist only within a very short distance from a boundary or interface between two materials with different refractive indices. They are also called near-field waves or tunneling waves. When a beam of light hits an interface between two materials, a portion of the light is reflected while another portion undergoes transmission. At the interface, the transmitted light creates an evanescent wave, which decays exponentially with distance from the interface at which the wave is formed. These oscillating waves penetrate tens of nanometers especially through a surface where total internal reflection occurs. Evanescent waves are important in many applications, such as optical microscopy, optical communication, and surface plasmon resonance sensing.

When an electromagnetic wave propagates through a medium, it can give rise to an evanescent field. The evanescent field is characterized by exponentially decaying amplitude with distance from the boundary, and it cannot be observed in the far field because its amplitude falls off too rapidly. The electromagnetic field only exists close to the boundary of the medium. It does not persist independently of the incident and reflected field. It only fulfills the electromagnetic boundary conditions. They are important in understanding the behavior of light at the interface between materials with different refractive indices, such as in optical waveguides and resonators. This wave field also occurs in the context of optics and other types of electromagnetic radiation, acoustics, and quantum mechanics.

Evanescent waves contain energy confined to a small region around the boundary. In contrast to the propagating waves, their amplitude decays exponentially with distance from the boundary. They do not contribute to the radiative transfer of energy and are non-sinusoidal solutions to Maxwell's equations. The existence of this evanescent field is significant in fiber optics, where light is confined to a thin glass fiber by total internal reflection.

When the light field travels through a medium of higher refractive index than the surrounding medium, some light rays are (internally) reflected from an interface at an angle greater than the critical angle resulting in total internal reflection occurs.  

The angle of incidence and angle of refraction are related by Snell’s law

n1 = lower refractive index medium

n2 = higher refractive index medium

θi = incident angle

θt = transmitted angle

The angle of incidence at which the transmitted wave is just grazing the boundary is the critical angle, θc

If θi  = θc, then θt = 90°

 

If θi  > θ

Hence θis an imaginary angle of refraction that doesn’t exist.

Where,

Thus, the incident light is fully reflected back into the medium from which it originated. When there is a complete reflection of the incident wave in the first medium, no part of the wave is propagated into the second medium. This represents a discontinuity in the EM fields at the interface. However, Maxwell's boundary conditions do not permit a discontinuity at the interface. In other words, the field immediately outside the medium cannot be zero. Instead, there must be some EM field that does not propagate and decays quickly in magnitude normal to the interface.

No energy is lost due to the evanescent wave unless absorbed in the medium it travels. Therefore, the energy in the reflected wave is equal to that of the incident wave. By conservation of energy, there can be no propagating transmitted wave, which would necessarily transfer energy away from the medium.

Evanescent waves can be mathematically characterized by a wave vector where one or more of the vector's components has an imaginary value. The electric field can be described as 

E0 is the wave propagation along the interface

Ei(Kx x̂ - iωt) is the time dependence of the wave

e-Keva ẑ is the exponential decay of the amplitude of the wave propagating along the interface

The above equation describes the wave traveling in the x-direction along the boundary direction.

The net energy flow of electromagnetic energy is given by the average Poynting vector, which is zero.

The polarization of the evanescent wave depends on the incident wave.

  • The parallel polarization, where the evanescent field spins along the interface, is more intense than the perpendicular.
  • Both can be greater than the incident intensity. 
  • For an s-polarized incident wave, the polarization remains s-polarized but has a phase lag.

Fiber Optics


In an optical fiber, the light reflects at angles near the critical angle, and a significant portion of the power extends into the cladding medium. The extended power turns out to be evanescent waves. The evanescent wave has been exploited to allow for real-time interrogation of surface-specific recognition events. It has applications in fiber optic biosensors, which utilize the concept of total internal reflection. In fiber, the light transits the optical fiber by repeatedly reflecting off the cladding-core interface. The penetration depth describes the distance the evanescent field extends beyond the core-cladding interface. The distance decreases to 1/e of its value at the core-cladding interface. 

The penetration depth is given by the equation:

Where x is distance from the fiber core, starting at x = 0 at the core-cladding interface E0 is the magnitude of the field at the interface

dp is the penetration depth.

Applications of Evanescent Waves

Evanescent waves have important applications in fiber optics and other fields, including:

  • Optical microscopy: Total internal reflection fluorescence microscope uses evanescent waves to study the surface properties of biological samples
  • Chemical sensing: Used in microscopy to illuminate small objects such as biological cells or DNA molecules.
  • Surface plasmon resonance: To excite surface plasmons at a resonant incident angle
  • Used in photonic and nanophotonic devices to sample volume outside a waveguide for sensing
  • Evanescent wave coupling and sensors

Evanescent Wave Coupling 


Evanescent wave coupling is a term used to describe how an electromagnetic wave can be coupled and sent from one system to another using a degrading electromagnetic field. To achieve coupling, two or more electromagnetic elements, such as optical waveguides, resonators, antennas, etc. are placed close together. This minimizes the amount of time that the evanescent field generated by one electromagnetic element decays before it reaches the other element. The evanescent field creates propagating wave modes in waveguides. These modes link or couple the wave from one waveguide to the next, provided that the receiving waveguide can support modes of the proper frequency.

In quantum mechanics and optics, evanescent waves are connected to quantum tunnelling phenomena. It is a barrier penetration of wave functions.

Evanescent Wave Sensors


Evanescent wave sensors are optical fiber sensors that work by detecting changes in the refractive index of a material near the sensor surface. In these sensors, the light is usually guided along the surface of a waveguide, such as an optical fiber or a planar waveguide, to obtain enough sensitivity. When a material with a higher refractive index than the waveguide is placed near the waveguide surface, the evanescent wave extends into the material. The interaction with the material leads to a change in the intensity or phase of the guided light. This change can be measured to determine the material's properties, such as its refractive index, thickness, or binding affinity to a specific molecule.

The main problem of this kind of sensor is the low interaction between the evanescent field and the quantity to be measured (measurand). In terms of waveguides, the interaction is proportional to the depth of the penetration in the cladding. This depth is related to the opto-geometrical parameters of the fibers, which are summed up in the normalized frequency ‘V’. The higher the ‘V’ value is, the deeper the penetration in the evanescent field is.

In these sensors, the protective plastic jacket of the fiber has been removed and the cladding has been reduced by polishing or by chemical means. As a result, the detection of chemical species becomes straightforward by carefully selecting the wavelength for operation. The measurand can be detected through the absorption of the evanescent wave, creating leakages and modulating the light intensity.

Special fibers, like D-fibers or micro-structured fibers are used to increase the interaction with the evanescent field. It is also possible to sharpen the fiber by heating it to its softening temperature and then by stretching it. It is common to adjust the thickness of the cladding, opting for a thinner or larger layer, in order to accommodate the variations in the optical characteristics of the substance being detected. This modification directly affects the behavior of the evanescent wave, which is sensitive to the properties of the surrounding medium.

Applications of Evanescent wave sensors

Evanescent wave sensors are commonly used in biochemical sensing applications, such as in detecting the presence of specific biomolecules in a sample, as well as in environmental monitoring and industrial process control.

  • Biosensing: These sensors are often used for label-free detection of biomolecules, such as proteins, DNA, and small molecules. It can detect changes in the sample's refractive index caused by binding the target molecule to a specific receptor on the sensor surface.
  • Environmental monitoring: To detect and measure various pollutants and contaminants in water, air, and soil. They can also detect changes in the chemical composition of a sample, such as pH, temperature, and humidity.
  • Industrial process control: Real-time monitoring of industrial processes, such as in the food and beverage industry, pharmaceutical manufacturing, and oil and gas exploration. The sensors can detect changes in the composition of the process media, such as the concentration of specific chemicals or the presence of impurities.
  • Medical diagnostics: For early detection and diagnosis of cancer and infectious diseases. It can detect changes in the concentration of specific biomarkers in blood, saliva, or urine, which indicate disease or infection.