KERR EFFECT IN OPTICS

The Kerr effect, in geometric optics, is an extension of laws of the light refraction at the time of its propagation in transparent materials with variable refractive indices. This effect took lately a considerable importance in the Industry of telecommunications with optical fibers. (Variable refractive index fibers).

The Kerr effect is used to avoid the chromatic scattering at the time of the transmission of light. It has for consequence to preserve, all along the course, relations of phases in the specter of the transmitted light, and therefore to avoid the deterioration of information. (Soliton)

In astrophysics it could be revealed of an unexpected importance in the gaseous environments having a gradient of refractive index, in interrelationship with gradient of matter density (gas). Especially when these environments are associated with the presence of gigantic black holes. (cores of galaxies)

Optical Laws of Descartes. (recalls)

The incidental ray, the perpendicular to impact and the refracted ray are in a same plan.

The sinus of the angle of incidence is in a constant report with the sinus of the angle of refraction. That is expressed with the relation:

sin i = n.sin r       (n is the refractive indice)

Let's note that the refractive index also depends of the frequency of the incidental wave. It is this property that is used in fibers with gradient of indice to avoid the chromatic scattering.

Kerr effect in plane geometry.

When light crosses an environment whose refractive indice believes continuous manner, light follows a trajectory whose angle varies continuously. In the example, opposite, one sees that light quickly tend toward the vertical axis.

Kerr effect in circular or spherical geometry.

In a spherical environment with a refractive indice, increasing from outside of the sphere toward the center of the sphere, light, entering in the sphere, follows a spirally trajectory. The type of spiral depends on the law of growth of the indice (linear, x², x3...)

Algorithm of simulation:

We achieved this simulation while writing a program in C " language ". The execution time, after compilation, was, on the PC of which we owned at this time (486 DX 50), of the order of half an hour.

We used, on advices of Mr. J.C. Pecker, Professor in the Collège de France, the perfect gas law, which permits to calculate the refractive indice, knowing n the density (Nb of molecules in the volume).

For the calculation of the refractive indice I took the equation therefore:

N²(v) = e(v) = 1 + 4pna(v)   With a = 0,91 (Hydrogen) et v = frequency

Then, We inserted it, in a software buckle containing the 2eme law of Descartes. The difficulty of the simulation is essentially due to the few of mathematical processor precision in the PCs. (Trigonometric tables, and numerical computations where, at this time, 32 bits limited. it is therefore better to achieve them with our own programs). besides don't forget the rounded of calculations. In final here is the result in the case of a sphere of gas of about hundred years light with a density varying from 10^-20 g/cm3 to 10^-10 g/cm3. The utilized growth law is in x². Alone the central part is represented here. Also notice that the simulation shows that the optical frequency has a negligible role in densities of matter placed in game.

Not to hide anything, when I undertook this work, no one believed there, me either.

Conclusion

If in the universe phenomena of refractivity are so, possible in a gas bubble with gradient of density of matter and with refractive indice, then, well evidently, it is strictly useless to invoke, for every case of lens, some and solely gravitational lens. However, the two phenomena are not certainly exclusive one of the other. And, in this case they are accomplice and cumulative !

Documents:

gradient d'indice (French)