Evanescent Waves

1
Evanescent Waves

• BMEN 489/689
• Spring 2006

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Evanescent Waves

• Evanescent waves are electromagnetic waves that
  penetrate tens of nm through a surface and
  propagate along the surface
• They may be used to sample volume outside a
  waveguide for sensing
• They may be used to locally excite a sample on
  the other side of an interface for imaging
  TIRF, DCPM

3
EM Review Polarization

• Light is a transverse electromagnetic wave
• This means the electric and magnetic wave
  oscillate orthogonal to the direction of motion
• The electric, or E, field can oscillate in the
  plane or out of the plane
• This defines linearly (or planar) polarized light

4
EM Review

• What happens when an EM wave hits a boundary
  between dielectric materials?
• The tangential components of E and H must be
  continuous across the boundary
• EiErEt
• The choice of E and H sign convention is arbitrary

i
r
E
E
H
H
n0
n1
E
H
t
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EM Review

• For normal incidence, this yields the familiar
  Fresnel intensity coefficients
• where It TI0, Ir RI0, I0 is the incident
  intensity, Ir is the reflected intensity and It
  is the transmitted intensity
• Note the RT1 and I /E/2

6
EM Review
E

• At oblique incidence, things get a little more
  interesting

i
r
H
?0
E
H
n0
n1
E
?1
H
t

• where R /r/2 and T/t/2(n1cos?1/n0cos?0)
• We also have Snells law
• n0sin?0 n1sin?1

7
EM Review

• If n0 gt n1, we have ?1 gt ?0 i.e. the transmitted
  angle will be greater than the incident angle
• At some critical angle, ?0 ?c, the transmitted
  angle will be 90º
• ?c sin-1(n1/n0)
• glass (n1.5)/H2O (n1.33) ? ?c 63º
• At this angle and beyond (? gt ?c), all the light
  will be reflectedTotal Internal Reflection

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Evanescent Waves

• However, those pesky boundary conditions still
  exist tangential components of E and H must be
  continuous across boundary
• This leads to a an evanescent wave that
  penetrates a small distance into the medium, n1.
  
• This wave propagates parallel to the surface

z
propagation direction
n1
n0
? gt ?c
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Evanescent Waves

• The wave decays exponentially with distance from
  the interface
• The distance is dependent upon the angle of
  incidence and wavelength generally lt ?0

z
propagation direction
n1
n0
? gt ?c
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Evanescent Waves

• The distance is not dependent on the polarization
  of the light
• However, the intensity at the interface is
  polarization dependent

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Evanescent Waves

• The parallel polarization is more intense than
  perpendicular, but both can be greater than the
  incident intensity

Simulation for n0 1.5 and n1 1.33
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Evanescent Waves

• The polarization of the evanescent wave depends
  on the incident wave
• For an s-polarized incident wave, the
  polarization remains s-polarized, but has a phase
  lag, d-

d-
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Evanescent Waves

• For parallel polarization, the polarization of
  the evanescent field cartwheels along the
  interface

d//
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Goos-Hanchen Shift

• The existence of the phase lags, d// and d-, give
  rise to a measurable longitudinal shift of a
  finite beam called the Goos-Hanchen shift
• Valid for ? ?c
• Physically we can view this as energy crossing
  the interface, flowing along surface and
  re-entering

s
? gt ?c
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Goos-Hanchen Shift

• As ???c, the shift gets larger
• As ??p/2, the shift is a small fraction of the
  wavelength