Transcript Circularly polarized waves

c = 300.000 km/sec
IF = I0 x (cosθ)2
Superposition of two waves:
1) same amplitude and wavelength,
2) polarized in two perpendicular planes,
3) oscillate in the same phase.
Superposition of two waves:
1) same amplitude and wavelength,
2) polarized in two perpendicular planes,
3) oscillate with 90o phase difference.
A phase difference of 90° means that when
one wave is at its peak then the other one is
just crossing the zero line.
Special electromagnetic wave. At any fixed point in space that is in the line of the propagation of
this wave, the electric field vector rotates in a circle while its length remains constant. Such
waves are called Circularly polarized waves. As the 3D picture shows, a circularly polarized wave
can be visualized with a spiral line; the wave propagates as a function describing a spiral instead
of one describing a sinus curve.
Superposition of two waves:
1) same amplitude and wavelength,
2) polarized in two perpendicular planes,
3) oscillate with -90o phase difference.
Superposition of two circularly polarized light beams:
1) same amplitude and wavelength,
2) Left and right polarised waves,
Any plane polarized light wave can be obtained as a superposition of a left circularly polarized
and a right circularly polarized light wave, whose amplitude is identical
The interaction of light and matter
If light enters matter, its properties may change. Namely, its intensity (amplitude), polarization,
velocity, wavelength, etc. may alter. The two basic phenomena of the interaction of light and
matter are absorption (or extinction) and a decrease in velocity.
Absorption means that the intensity (amplitude) of light decreases in matter because matter
absorbs a part of the light. (Intensity is the square of amplitude.)
The decrease in velocity (i.e. the slowdown) of light in matter is caused by the fact that all
materials (even materials that do not absorb light at all) have a refraction index, which means
that the velocity of light is smaller in them than in vacuum. The refraction index is the ratio of
the velocities of light measured in vacuum and in the given material.
A plane-polarized wave traverses a medium that absorbs light but does not refract it
(refraction index= 1)
After exiting the material, the field vector oscillates the same way as before entering it but its
amplitude is only about 36% of the earlier value.
A circularly polarized wave traverses a medium that absorbs light but does not refract it
(refraction index= 1)
After exiting the material, the field vector oscillates the same way as before entering it but its
amplitude is only about 36% of the earlier value.
A plane-polarized wave traverses a medium that does not absorb light but refracts it
(refraction index> 1)
When the light beam enters the piece of material, it slows down because the refracting index of
the material is greater than 1.0. Its ν does not change, therefore its λ decreases (the product of
the frequency and the wavelength should be equal to c). In these animations, we used a
refraction index n=2.2. This means that in c the medium is 1/2.2 times the c in vacuum, and its
λ also decreases to 1/2.2 times the original value.
The two field vectors at the intersecting planes do not oscillate in the same phase any longer
A circularly polarized wave traverses a medium that does not absorb light but refracts it
(refraction index> 1)
The two field vectors at the intersecting planes do not oscillate in the same phase any longer
Some materials possess a special property: they absorb left circularly polarized light to a
different extent than right circularly polarized light. This phenomenon is called circular
dichroism.
REMEMBER: Any plane polarized light can be obtained as the superposition of a left circularly
polarized and a right circularly polarized light wave.
If linearly polarized light traverses a medium that shows circular dichroism, its properties will
change (the medium absorbs the two circularly polarized components to a different extent.)
e.g.
Does NOT absorb red
Highly absorbs green
The red component traverses the medium
unchanged while the green gets fainter: its
intensity decreases to ~ 36% of the original value.
The superposition of the two components is no
longer a linearly polarized wave: the resulting field
vector does not oscillate along a straight line but it
rotates along and ellipsoid path. Such a light wave
is called an elliptically polarized light.
The big axis of the ellipse is parallel to the polarization plane of the original light wave. This is
always the case, regardless of which circular component is absorbed more by the medium
Of course, it is very unusual for a material not to absorb one circular component at all. Real
materials usually absorb both components, to a different extent
How elliptical the plane-polarized wave becomes after traversing the medium is determined by
the difference between the absorptions of the two circularly polarized components. In the
most extreme case, the material almost completely extincts one component--and then the
plane-polarized wave almost becomes a perfect circularly polarized light because the other
circular component disappears.
circular dichroism makes plane-polarized light elliptically polar
There are materials having another special property: their refraction index is different for
left and right circularly polarized light. This phenomenon is called circular birefringence.
A plane-polarized light wave
(indicated by light blue
color) traverses a medium
that does not slow down
the left circularly polarized
component (this is the
circular wave shown in red)
of the wave at all but slows
down the right circularly
polarized component (this is
the circular wave shown in
green) somewhat (n=1.05).
circular birefringence rotates the plane of
polarization of plane-polarized light.
The component shown in red traverses the medium unchanged while the component shown in
green gets slower and its wavelength decreases in the medium. This slowdown and the
decreased wavelength is hard to see in the figure because the refraction index (1.05) is close to
1.0. But as a result of this refraction index, the wave shown in green makes 4.2 full periods in
the medium instead of 4 full periods, therefore its field vector will further on its rotating path
than if the medium were not present
circular birefringence rotates the plane of
polarization of plane-polarized light.
In reality, it rarely occurs that a material exhibits circular dichroism but no circular birefringence
or it exhibits circular birefringence but no circular dichroism with respect to light of a certain
wavelength.
The incident light suffers two
modifications here:
1) because of the circular
dichroism, it becomes
elliptical;
2) because of the circular
birefringence, its polarization
gets rotated.
Since the exiting light is no longer
plane-polarized, it is not the
plane of polarization that gets
rotated but the big axis of the
ellipse of polarization of the
elliptically polarized light.
The ellipticity of the light exiting the medium is determined by the difference between the
absorptions with respect to the left and right circularly polarized components. The angle made
by the big axis of the ellipse with respect to the original polarization plane is determined by
the difference between the refraction indices with respect to the left and right circularly
polarized components.
With the appropriate instrument, the ellipticity and the angle of rotation of the polarization
plane of light can be measured. From those data, the difference between absorptions and
refraction indices with respect to left and right circularly polarized lights can be calculated.
Circular dichroism and circular birefringence are caused by the asymmetry of the molecular
structure of matter. The optical activity of solutions of biological macromolecules provides
information about the structural properties of the macromolecules