In Out Material having different
extinction coefficients for right and left circularly polarized lights: R and L
Plane-polarized light becomes elliptically polar
) 90 /
2
In Out Material having different
refraction indices for right and left circularly polarized lights: nR and nL
The plane of polarization of plane-polarized light gets rotated
) 90 /
2 sin(
) 90 /
2
sin(
R
L
A n x t A n x t
E
y
) /
2 sin(
) /
2
sin( nR x t A n x t
A
Ez
L
Circular birefringence
In Out Material having different
extincion coefficients AND refraction indices for right and left circularly polarized lights: R and L AND nR and nL
Plane polarized light gets elliptically polar, with the great axis of the ellipse being rotated relative to the original plane of polarization
) 90 /
2 sin(
) 90 /
2
sin(
R
L
Ae
n x t Ae
n x t
E
y Rx
Lx
) /
2 sin(
) /
2
sin( n
Rx t Ae n
Lx t
Ae
E
z
Rx
Lx
Circular dichroism and birefringence
•
Rayleigh•
Mie•
GeometricThe process whereby EM radiation is absorbed and immediately re-emitted by a particle or molecule – energy can be emitted in multiple-directions
The type of scattering is controlled by the size of the wavelength relative to the size of the particle
Light scattering
NOON
• less atmosphere
• less scattering
• blue sky, yellow sun
SUNSET
• more atmosphere
• more scattering
• orange-red sky & sun
• Molecules in atmosphere scatter light rays.
• Shorter wavelengths (blue, violet) are scattered more easily.
Light scattering
Blue sky and red sunset
•
Wavelength of light is much larger than scattering particles,•
Blue light ~4000 Angstroms, scattering particles ~1 Angstrom (1A=10-10 m)Rayleigh scattering
•
Occurs when the wavelength ≅ particle size,•
Explains scattering around larger droplets such as Corona around the sun or moon, Glory and similar phenomena.•
Occurs with particles that are actually 0.1 to 10 times the size of the wavelength•
Primary Mie scatterers are dust particles, soot from smoke•
Mie scatterers are found lower in theTroposphereMie scattering
Rayleigh and Mie scattering
•
The dependence of wave speed and index of refraction on wavelength is called dispersion,•
The index of refraction depends on the frequency of the light: the higher the frequency, the higher the index of refraction,•
Because white light is a mixture of frequencies, different wavelengths travel in different directions.•
Dispersion is the cause of chromatic aberration in a simple lens:•
Different colours focus at different points,•
It’s a common defect of simple lenses,•
Sometimes you see a fringe of colours around an image seen through a lens or a telescope,•
Chromatic aberration can be corrected by combining two or more lenses.Dispersion
• 1665-1666 – First experiment of Isaac Newton with dispersion, experimentum crucis
• For this distribution of colours Newton coined the term spectrum,
• White light can be dispersed into different wavelengths,
• Dispersed ray (monochromatic) cannot be divided into other wavelengths
Dispersion
*
Slit Slit
• White light is a “Heterogeneous mixture of different refrangible Rays”
• Colours of the spectrum cannot be individually modified.
• Colours are “Original and connate properties, which in divers Rays are divers. Some Rays are disposed to exhibit a red colour and no other; some a yellow and no other, some a green and no other, and so of the rest”.
Dispersion – Newton’s conclusions
*
•
In the presence of dispersion, wave velocity is no longer uniquely defined, giving rise to the distinction of phase velocity and group velocity.•
A well-known effect of phase velocity dispersion is the color dependence of light refraction that can be observed in prisms and rainbows.•
Dispersion may be caused either by geometric boundary conditions (waveguides, shallow water) or by interaction of the waves with the transmitting medium.Dispersion
•
is the phenomenon in which the phase velocity of a wave depends on itsfrequency, or alternatively when the group velocity depends on the frequency.
•
Media having such a property are termed dispersive media. Dispersion is sometimes called chromatic dispersion to emphasize its wavelength-dependent nature, or group-velocity dispersion (GVD) to emphasize the role of the group velocity.•
Dispersion is called normal when the refractive index decreases with the wavelength,•
For materials with selective absorption the refractive index can increase in some selective wavelength ranges…•
This kind of dispersion is called anomalous.Dispersion
Refractive index (n)
•
A rainbow is caused by the dispersion of light in droplets of rain.•
When sunlight enters a drop, it is separated into its coloured components.• The final direction of light is quite opposite to its incident direction.
• Violet light changes its direction by 320°.
• Red light changes its direction by 318°.
Dispersion
•
In a range of absorption maximum, the refractive index can be even <1,•
it means that for 0<n<1 the wave speed:• There is no paradox in it.
• Phase velocity is the rate at which the phase of the wave propagates,
• It this does not indicate any superluminal information or energy transfer,
Phase velocity
Phase velocity
•
The group velocity of a wave is the velocity with which the overall shape of the wave's amplitudes — known as the modulation or envelope of the wave— propagates through space.
• The group velocity is often thought of as the velocity at which energy or information is conveyed along a wave.
• In most cases this is accurate, and the group velocity can be thought of as the signal velocity of the waveform.
• However, if the wave is travelling through an absorptive medium, this does not always hold.
Group velocity
•
various experiments have verified that it is possible for the group velocity of laser light pulses sent through specially prepared materials to significantly exceed the speed of light in vacuum,•
However, superluminal communication is not possible in this case, since the signal velocity remains less than the speed of light.•
It is also possible to reduce the group velocity to zero, stopping the pulse, or have negative group velocity, making the pulse appear to propagate backwards.•
However, in all these cases, photons continue to propagate at the expected speed of light in the medium•
1999 Rowland Institute for Science, Cambridge,•
2000 NEC Research Institute, Princton,Group velocity (equal to an electron's speed) should not be confused with phase velocity (equal to the product of the electron's frequency multiplied by its
wavelength).
Phase and group velocity
•
In a dispersive medium, the phase velocity varies with frequency and is not necessarily the same as the group velocity of the wave, which is the rate at which changes in amplitude (known as the envelope of the wave) propagate.•
In some specific cases the phase velocity has a negative sign as group velocity.moves with the phase velocity, moves with the group velocity