On 20 July 2000 issue of magazine Nature, 3 scientists Wang, Kuzmich and Dogariu talked about transmission faster than light. But, in reality it is just anomalous dispersion, as the scientists readily say yes to. A light pulse is decomposed into a sum of sine waves having different wavelengths, the graphs of which are shown below.
The sum of the red, green and blue sine waves is shown by the black waves. As all of the waves get delayed, but the longer wavelengths i.e. red are delayed more and the shorter wavelengths i.e. blue are delayed less, then the overall pulse seems to be advanced in time!
In the same way, the pulse in the Wang et al. experiment was advanced by 62 nanoseconds while passing through a gas cell which was only 6 cm in length. Even if the speed of transmission was infinite, that could only saved 0.2 nanoseconds off the time. The actual advance was much more, representing that time traveled into the past, not faster than light travel. But in reality it was only anomalous dispersion. In normal dispersion in glass blue light delays more than the red light, on the other hand in anomalous dispersion the red light is delayed more than the blue. Due to this the pulse peak shifts earlier in time.
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Waves in a Dispersive Medium
Dispersion causes the shape of a wave pulse to change as it travels
In case the wave speed depends only on the physical properties of the medium then the wave speed is a constant. It becomes independent of frequency. Such a medium is called a non-dispersive medium. The waves travelling through this medium will maintain a constant shape. The pulse is a Gaussian function, containing multiple frequencies. As the wave speed is constant, all frequencies travel at the same speed so the pulse maintains constant shape.
However, there are examples of dispersive media where, the wave speed depends on the frequency of the wave. The blue wave pulse in the animation is the same Gaussian function as the black pulse. It consists of a large number of frequency components which are added together. Now the wave speed directly depends on frequency, with higher frequencies travelling faster than the lower frequencies. As a result of which, the wave pulse spreads out and it changes its shape as it travels.
The "centres" of both wave pulses travel at the same speed in same direction. This fact lead in formation of the concept of "group velocity". It states that the speed with which the energy carried by the wave travels. The group velocity remains the same for each wave pulse.
Dispersion for a wave packet with many frequency components
Let a wave packet built up from a sum of 100 cos functions with different frequencies. In a non-dispersive medium all the components of different frequency travel at the same speed so the wave function doesn't change at all as it travels.
We have the same wave packet, built up from a sum of 100 cos functions with different frequencies. As now the medium is dispersive so different frequency components travel at different speeds. In this way the wave changes shape. We could see the group velocity and the phase velocity. For example, the dispersion is in such a way that lower frequencies travel faster than higher frequencies. As a result of this, the wave packet spreads out with the longer wavelengths moving faster and the shorter wavelengths remaining behind.
Low dispersion glass
Low dispersion glass is a glass having low dispersion. Crown glass is such example of a relatively inexpensive low-dispersion glass.
Two kinds of low dispersion glasses are special low dispersion glass-SLD glass and extraordinary low dispersion glass-ELD glass. But still they have very high prices. Other kinds of glasses are extra-low dispersion glass-ED glass, and ultra-low dispersion glass-UL glass
Main use of low dispersion glasses is particularly to reduce chromatic aberration. Most oftenly they are used in achromatic doublets. The positive element is made up of a low-dispersion glass; the negative element is made from a high-dispersion glass. To oppose the effect of the negative lens, the positive lens is made thicker. Therefore chromatic doublets have higher thickness. They have more weight than the equivalent non-chromatic-corrected single lenses.
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In comparison to telephoto lenses, shorter focal length objectives have less benefit as compared to low dispersion elements, as their chief problem is spherical aberration instead of chromatic aberration. The spherical aberration introduced by the LD elements can be corrected with a spherical lens. The SLD elements provide increased sharpness which allows using lower f-numbers and this results in faster shutter speed. This is critical. For e.g., it is used in sports photography and wildlife photography. The shallow depth of field provided by a telephoto lens also allows the subject of the photography to stand out better against the background.
Low dispersion glasses are also employed in handling ultra short pulses of light, in e.g. mode-locked lasers, in order to prevent pulse broadening by group velocity dispersion in the optical elements.
Some glasses have a peculiar property called anomalous partial dispersion. Their use in long focal length lens assemblies was pioneered by Leitz. Before their availability, calcium fluoride in the form of fluorite crystals were used as material for these lenses; however the low refraction index of calcium fluoride required high curvatures of the lenses, therefore increasing spherical aberration. Fluorite also has poor shape retention and is very fragile. Abnormal dispersion is required for design of apochromat lenses.
Glass with addition of thorium dioxide has high refraction and low dispersion and was in use since before World War II (WW2), but its radioactivity led to its replacement with other compositions. Even during WW2, Kodak managed to make high-performance thorium-free optical glass for use in aerial photography, but it was yellow-tinted. In combination with black and white film, the tint helped in acting as a photographic filter improving contrast.
In Leitz laboratories a discovery was made that lanthanum (III) oxide can be a suitable replacement thorium dioxide. For preserving amorphous character of the glass and prevent crystallization some other elements had to be added that would cause striate defects.
George W. Morey introduced the lanthanum oxide and oxides of other rare earth elements in borate glasses after 1930. This greatly expanded the available range of high-index low-dispersion glasses. Borate glasses have lower wavelength-refraction dependence in the blue region of spectrum than silicate glasses with the same Abbe number. These "borate flint" glasses, or KZFS, are highly susceptible to corrosion by acids, alkalis, and weather factors. Naturally borate glass with more than 20Â mole % of lanthanum oxide is very durable under ambient conditions. The use of rare earth elements allowed development of high-index low-dispersion glasses of both crown as well as flint types.
All high-performance glasses contain high content of zirconium dioxide. Its high melting point requires use of crucibles lined by platinum to prevent contamination with crucible material.
A great high-refraction replacement for calcium fluoride(CF) as a lens material can be a glass made of fluorophosphates. In this, a proportion of fluorides is stabilized with help of a metaphosphate, with addition of titanium dioxide.
Several of the above mentioned high-performance glasses are very expensive because highly pure chemicals must be produced in substantial quantities.
Change ofÂ index of refractionÂ with wavelength is called chromatic dispersion. In general, the refractive index of light decreases as wavelength increases. Blue light travels more slowly in the material than red light. Red light has more speed than blue light. Dispersion is the phenomenon which gives you theÂ separation of colorsÂ from white light in aÂ prism. It also gives the generally unwanted chromatic aberrationÂ in lenses. Usually the dispersion of a material is measured by measuring the index at the blue F line of hydrogen having wavelength 486.1 nm, the yellow sodium D lines with wavelength 589.3 nm, and the red hydrogen C line with wavelength 656.3 nm. Usually the dispersion is measured by a standard parameter which is known as Abbe's number, or the v value or V number, all of them refer to the same parameter:
Data from Serway & Jewett
NOTE:Blue light travels more slowly than red light in transparent media.
By calculating the change in the focal length with wavelength, the effect of dispersion on the focal length of a lens can be checked. The table made below starts with a biconvex lensv aand is designed to have a focal length of 10.0 cm for violet light which has wavelength of 400 nm falling on crown glass. The focal lengths shown are calculated from theÂ lensmakers equationÂ with radii of curvature 10.62 cm for both surfaces.
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Chromatic aberration arising from dispersion.
Separation of colors by a prism is an example of dispersion
Types of DISPERSION
Two types of dispersion observed in optical fibres are:-
Intramodal, also known as chromatic dispersion occurs in all kinds of fibers.
Intermodal, also known as modal dispersion occurs only in multimode fibers.
Due to every type dispersion mechanism pulse spreading is spread. As a pulse spreads, energy is overlapped. This condition is shown in figure 2-24. The spreading of the optical pulse as it travels along the fiber limits the information capacity of the fiber.
Intramodal, or chromatic, dispersion depends primarily on fiber materials. There are two types of intramodal dispersion. The first type is material dispersion. The second type is waveguide dispersion.
Intramodal dispersionÂ occurs because different colors of light travel through different materials and different waveguide structures at different speeds.
Material dispersionÂ occurs because the spreading of a light pulse is dependent on the wavelengths' interaction with the refractive index of the fiber core. Different wavelengths travel at different speeds in the fiber material. Different wavelengths of a light pulse that enter a fiber at one time exit the fiber at different times. Material dispersion is a function of the source spectral width. The spectral width specifies the range of wavelengths that can propagate in the fiber. Material dispersion is less at longer wavelengths.
Waveguide dispersionÂ occurs because the mode propagation constant (&beta ;) is a function of the size of the fiber's core relative to the wavelength of operation. Waveguide dispersion also occurs because light propagates differently in the core than in the cladding.
In multimode fibers, waveguide dispersion and material dispersion are basically separate properties. Multimode waveguide dispersion is generally small compared to material dispersion. Waveguide dispersion is usually neglected.
However, in single mode fibers, material and waveguide dispersion are interrelated.
The total dispersion present in single mode fibers may be minimized by trading material and waveguide properties depending on the wavelength of operation.
Q.46 Name the two types of intramodal, or chromatic, dispersion.
Q.47 Which dispersion mechanism (material or waveguide) is a function of the size of the fiber's core relative to the wavelength of operation?
Intermodal or modal dispersion causes the input light pulse to spread. The input light pulse is made up of a group of modes. As the modes propagate along the fiber, light energy distributed among the modes is delayed by different amounts. The pulse spreads because each mode propagates along the fiber at different speeds. Since modes travel in different directions, some modes travel longer distances.Â Modal dispersionÂ occurs because each mode travels a different distance over the same time span, as shown in figure 2-25. The modes of a light pulse that enter the fiber at one time exit the fiber a different times. This condition causes the light pulse to spread. As the length of the fiber increases, modal dispersion increases.
Modal dispersion is the dominant source of dispersion in multimode fibers. Modal dispersion does not exist in single mode fibers. Single mode fibers propagate only the fundamental mode. Therefore, single mode fibers exhibit the lowest amount of total dispersion. Single mode fibers also exhibit the highest possible bandwidth.
Q.48 Modes of a light pulse that enter the fiber at one time exit the fiber at different times. This condition causes the light pulse to spread. What is this condition called?