9.3 Reflection and Diffraction
261
When the wave enters the denser medium, it is diffracted towards the normal. If the wave propagates
into the less-dense medium (reversely to the situation shown in Fig. 9.3), a diffracted wave occurs only
up to a critical angle of incidence
sin φ TR =
n 2
n 1
.
(9.11)
For larger angles of incidence, total internal reflection occurs and the wave remains in the denser
medium. Thus, the angle in (9.11) is called the critical angle for total reflection. For GaAs and air the
critical angle is rather small, φ TR = 17.4
◦ .
The reflectance depends on the polarization (Fresnel formulas [834]). The index ‘p’ (‘s’) denotes
parallel polarized/TM (perpendicular polarized/TE) waves.
R p =
tan(φ − ψ)
tan(φ + ψ)
2
(9.12)
R s =
sin(φ − ψ)
sin(φ + ψ)
2
.
(9.13)
The situation for GaAs and air is shown for both polarization directions and unpolarized radiation in
Fig. 9.4 for a wave going into and out of the GaAs.
When the reflected and the diffracted wave are perpendicular to each other, the reflectance of the
p-polarized wave is zero. This angle is the Brewster angle φ B ,
tan φ B =
n 2
n 1
.
(9.14)
If a wave has vertical incidence from vacuum on a medium with index of refraction n r , the reflectance
is given (both polarizations are degenerate) as
Fig. 9.3 Reflection and
diffraction of an
electromagnetic wave at
the transition between
medium ‘1’ and ‘2’,
n 2 > n 1 . The polarization
plane is defined by the
surface normal and the
k-vector of the light (plane
of incidence). The parallel
(‘p’) polarized wave
(TM-wave, electric field
vector oscillates in the
plane) is shown as ‘↔’;
perpendicular (‘s’)
polarization (TE-wave,
electric field vector is
perpendicular to plane) is
depicted as ‘·’
261
When the wave enters the denser medium, it is diffracted towards the normal. If the wave propagates
into the less-dense medium (reversely to the situation shown in Fig. 9.3), a diffracted wave occurs only
up to a critical angle of incidence
sin φ TR =
n 2
n 1
.
(9.11)
For larger angles of incidence, total internal reflection occurs and the wave remains in the denser
medium. Thus, the angle in (9.11) is called the critical angle for total reflection. For GaAs and air the
critical angle is rather small, φ TR = 17.4
◦ .
The reflectance depends on the polarization (Fresnel formulas [834]). The index ‘p’ (‘s’) denotes
parallel polarized/TM (perpendicular polarized/TE) waves.
R p =
tan(φ − ψ)
tan(φ + ψ)
2
(9.12)
R s =
sin(φ − ψ)
sin(φ + ψ)
2
.
(9.13)
The situation for GaAs and air is shown for both polarization directions and unpolarized radiation in
Fig. 9.4 for a wave going into and out of the GaAs.
When the reflected and the diffracted wave are perpendicular to each other, the reflectance of the
p-polarized wave is zero. This angle is the Brewster angle φ B ,
tan φ B =
n 2
n 1
.
(9.14)
If a wave has vertical incidence from vacuum on a medium with index of refraction n r , the reflectance
is given (both polarizations are degenerate) as
Fig. 9.3 Reflection and
diffraction of an
electromagnetic wave at
the transition between
medium ‘1’ and ‘2’,
n 2 > n 1 . The polarization
plane is defined by the
surface normal and the
k-vector of the light (plane
of incidence). The parallel
(‘p’) polarized wave
(TM-wave, electric field
vector oscillates in the
plane) is shown as ‘↔’;
perpendicular (‘s’)
polarization (TE-wave,
electric field vector is
perpendicular to plane) is
depicted as ‘·’