Rasmus Bartholin is remembered especially for his discovery (1669) of the double refraction of a light ray by Iceland spar (calcite). He published an accurate description of the phenomenon, but since the physical nature of light was poorly understood at the time, he was unable to explain it. It was only after Thomas Young proposed the wave theory of light, c. 1801 that an explanation became possible.
Experiments with the double refracting Iceland crystal which led to the discovery of a marvelous and strange refraction,
tr. by Werner Brandt. Westtown, Pa., 1959.
Birefringence, or double refraction, is the decomposition of a ray of light into two rays (the ordinary ray and the extraordinary ray) when it passes through certain types of material, such as calcite crystals or boron nitride, depending on the polarization of the light. This effect can occur only if the structure of the material is anisotropic (directionally dependent). If the material has a single axis of anisotropy or optical axis, (i.e. it is uniaxial) birefringence can be formalized by assigning two different refractive indices to the material for different polarizations. The birefringence magnitude is then defined by
Birefringence can be observed in amyloid plaque deposits such as are found in the brains of Alzheimer's patients. what does this mean in regard to memory or subjectivity.
The laws of refraction (called Snell's Laws) were laid down by Willebrod Snellius in 1621 and he proposed the following formula:
(sine i)/(sine r) = n
Where i is the angle of incidence and r is the angle of refraction and n is the index of refraction. It turns out that this ratio n is also the ratio of the speed of light in air to the speed of light in the crystal. This relationship shows the impact of density or specific gravity to the index of refraction in that the greater the density the slower the speed of light. But density is not the only impact to the index of refraction (if it were, we could use index of refraction to measure density and we can't do that, directly anyway) as chemistry and structure play an important part too. Generally the index of refraction for minerals falls between 1.4 to 2.0 with a few exceptional mineral exceeding 2.5.
the difference between the highest and lowest indexes of refraction is the birefringence magnitude.
The symmetry of the crystal has interesting impacts to the index of refraction. Isometric and amorphous minerals have essentially the same structure or lack there of, in all directions and so have only one index of refraction and are called isotropic minerals. But hexagonal, trigonal and tetragonal minerals have a different structure along their primary axes than they do in all other directions and for this reason they have two indices of refraction; one along the primary axis and one for every other direction. These minerals are called uniaxial minerals for their one unique direction. Orthorhombic, monoclinic and triclinic minerals have two planes of equal refractive indices and are called biaxial.
http://www.rockhounds.com/rockshop/xtal/index.html
http://www.webmineral.com/crystall.shtml#hexagonal
http://www.webmineral.com/data/Calcite.shtml
CALCITE
The varieties of calcite, CaCO3, are so numerous and so varied that an entire display case at the Smithsonian Museum of Natural History is devoted to just calcite. Calcite is the most abundant of the carbonate minerals. The sample shown above and in the closeup view below is called cobaltian calcite. The sample is about 9x12 cm. samples are part of the gem and mineral exhibit at the Smithsonian Museum of Natural History.
The calcite gem above is 52.3 carats and is from Balmat, New York. . The large gem right is 1865 carats and is from Balmat, New York.
This huge single crystal of calcite is about 30x45 cm and is from Iceberg claim, Dixon, New Mexico. It shows the characteristic calcite geometry and shows the large birefringence of calcite in the double image of the text placed behind it.
Synthetic Crystals
How can I make a large synthetic crystal? A stone structure, a lens, a wedge, a prism, a film? what would the structure be? what would i use it for? painting, communication, light, sound, accessory?
utilitarian or utopian? fashion or function?
Polymer liquid crystals
Polymer liquid crystals (PLCs) are a class of materials that combine the properties of polymers with those of liquid crystals. A liquid crystal polymer can be seen as a network of conventional LC molecules that are linked together by polymerization.
The main advantage of these materials compared to inorganic crystals such as calcite or quartz is that it is inexpensive technology and can be easily shaped in any wanted geometry such as microlenses or wedges. The disadvantage is the lower optical quality due to enhanced scattering and defects. The use of PLC, as many other plastic optical components, is ideal for applications where low-cost robust birefringent elements are needed with modest quality requirements.
The polymerized liquid crystal forms a positive uniaxial birefringent material with an ordinary index of about 1.5 and an extraordinary index between 1.6 to 1.7 depending on the LC. The maximal birefringence that can be obtained is about ne-no= 0.2. Note that with this technology we are limited to a maximal thickness of 0.2 mm.
Birefringent wedges and Wollaston prisms
Birefringent wedges are useful for separating the
two polarization component of light.
When combining two wedges one can obtain a Wollaston prism, which double the splitting angle compared to the simple prism.
Actually we are able to manufacture prisms with splitting angles from 0° to 0.5°. Prism size (active area) can be comprise between 5x5mm and 20x20mm. Such prisms can be used for applications such as Differential Interference Contrast (DIC) microscopy.
Ask a polaroptic engineer for more information: info@arcoptix.com
Molding technique
With the unique molding technique developed by ARCoptix we are capable to manufacture on demand uniaxial birefringent elements of any geometry (diffractive elements, cylindrical or toroidal lenses...). However the maximal thickness of the elements should not exceed 0.2mm. This technology offers the possibility to combine ordinary diffractive optical element design with an additional degree of freedom:Polarization!
The molding (or replication) technique can essentially be divided in three steps:
1) Fabrication of the master. The master should be the copy of the wanted diffractive-refractive one wants to obtain with LC polymer. Master are usually realized by using ordinary photolithographic methods.
2) Fabrication of a PDMS stamp. A PDMS stamp can be obtain by casting the master with degassed liquid PDMS. The PDMS becomes solid by thermal polymerization.
3) Fabrication of the birefringent LC element. The liquid LC polymer is sandwiched between a substrate with an alignment layer and the PDMS stamp. When The LC is nicely aligned the LC molecules are linked together by UV curing. When removing the PDMS one obtain a plastic birefringent diffractive-refractive element.
Birefringent microlens arrays
A Birefringent lens produces two different focal points for the two polarization components as demonstrated in the figure below. ARCoptix can fabricate such birefringent microlenses arrays made of polymer nematic LC on demand. For more information: info@arcoptix.com.
Birefringent microlenses shows different focal points for each polarization component