Evanescent wave

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Schematic representation of evanescent waves propagating along a metal-dielectric interface. The charge density oscillations, when associated with electromagnetic fields, are called surface plasmon-polariton waves. The exponential dependence of the electromagnetic field intensity on the distance away from the interface is shown on the right. These waves can be excited very efficiently with light in the visible range of the electromagnetic spectrum.

An evanescent wave is a near-field wave with an intensity that exhibits exponential decay without absorption as a function of the distance from the boundary at which the wave was formed. Evanescent waves are a general property of wave-equations, and can in principle occur in any context to which a wave-equation applies. They are formed at the boundary between two media with different wave motion properties, and are most intense within one third of a wavelength from the surface of formation. In particular, evanescent waves can occur in the contexts of optics and other forms of electromagnetic radiation, acoustics, quantum mechanics, and "waves on strings".[1][2]

Evanescent wave applications[edit]







 k \propto \frac{1}{d} \ln{\frac{1}{\delta}},

where k is the maximum wave vector that can be resolved, d is the distance between the object and the sensor, and \delta is a measure of the quality of the sensor.

More generally, practical applications of evanescent waves can be classified in the following way:


Total internal reflection of light[edit]




 \mathbf{k} \ = \ k_y \hat{\mathbf{y}} + k_x \hat{\mathbf{x}}
\ = \ i \alpha \hat{\mathbf{y}} + \beta \hat{\mathbf{x}},



 \mathbf{E}(\mathbf{r},t) = \mathrm{Re} \left \{ E(\mathbf{r}) e^{ i \omega t } \right \} \mathbf{\hat{z}}

where \scriptstyle\mathbf{\hat{z}} is the unit vector in the z direction.


 E(\mathbf{r})  =  E_o e^{-i ( i \alpha y + \beta x ) }  =  E_o e^{\alpha y - i \beta x }

where α is the attenuation constant and β is the propagation constant.

Evanescent-wave coupling[edit]



Coupling is usually accomplished by placing two or more electromagnetic elements such as optical waveguides close together so that the evanescent field generated by one element does not decay much before it reaches the other element. With waveguides, if the receiving waveguide can support modes of the appropriate frequency, the evanescent field gives rise to propagating-wave modes, thereby connecting (or coupling) the wave from one waveguide to the next.

Evanescent-wave coupling is fundamentally identical to near field interaction in electromagnetic field theory. Depending on the impedance of the radiating source element, the evanescent wave is either predominantly electric (capacitive) or magnetic (inductive), unlike in the far field where these components of the wave eventually reach the ratio of the impedance of free space and the wave propagates radiatively. The evanescent wave coupling takes place in the non-radiative field near each medium and as such is always associated with matter; i.e., with the induced currents and charges within a partially reflecting surface. This coupling is directly analogous to the coupling between the primary and secondary coils of a transformer, or between the two plates of a capacitor. Mathematically, the process is the same as that of quantum tunneling, except with electromagnetic waves instead of quantum-mechanical wavefunctions.


See also[edit]


  1. ^ a b Tineke Thio (2006). "A Bright Future for Subwavelength Light Sources". American Scientist (American Scientist) 94 (1): 40–47. doi:10.1511/2006.1.40. 
  2. ^ a b Marston, Philip L.; Matula, T.J. (May 2002). "Scattering of acoustic evanescent waves...". Journal of the Acoustical Society of America 111 (5): 2378. Bibcode:2002ASAJ..111.2378M. 
  3. ^ Sreekanth, Kandammathe Valiyaveedu; Zeng, Shuwen; Shang, Jingzhi; Yong, Ken-Tye; Yu, Ting (2012). "Excitation of surface electromagnetic waves in a graphene-based Bragg grating". Scientific Reports 2. Bibcode:2012NatSR...2E.737S. doi:10.1038/srep00737. 
  5. ^ Zeng, Shuwen; Yu, Xia; Law, Wing-Cheung; Zhang, Yating; Hu, Rui; Dinh, Xuan-Quyen; Ho, Ho-Pui; Yong, Ken-Tye (2012). "Size dependence of Au NP-enhanced surface plasmon resonance based on differential phase measurement". Sensors and Actuators B: Chemical 176: 1128. doi:10.1016/j.snb.2012.09.073. 
  6. ^ Fan, Zhiyuan; Zhan, Li; Hu, Xiao; Xia, Yuxing (2008). "Critical process of extraordinary optical transmission through periodic subwavelength hole array: Hole-assisted evanescent-field coupling". Optics Communications 281 (21): 5467. Bibcode:2008OptCo.281.5467F. doi:10.1016/j.optcom.2008.07.077. 
  7. ^ Karalis, Aristeidis; J.D. Joannopoulos, Marin Soljačić (February 2007). "Efficient wireless non-radiative mid-range energy transfer". Annals of Physics 323: 34. arXiv:physics/0611063v2. Bibcode:2008AnPhy.323...34K. doi:10.1016/j.aop.2007.04.017. 
  9. ^ Wireless energy could power consumer, industrial electronicsMIT press release
  10. ^ Axelrod, D. (1 April 1981). "Cell-substrate contacts illuminated by total internal reflection fluorescence". The Journal of Cell Biology 89 (1): 141–145. doi:10.1083/jcb.89.1.141. PMC 2111781. PMID 7014571. 

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