Gradient Refractive IndexGradient Refractive Index

The refractive index of a particular point of a lens with a gradient refractive index

The refractive index of a particular point of in a lens with a radial gradient refractive index

The effects of gravitational potential as related to the effects of a refractive index

G.R.I.N. LENS

In reality we have multiple masses… Vector superposition!“The total deflection angle is the vector superposition of the deflections due to all the mass elements of the lens.” (Blandford et al. 825)

Angle of deflection: One ray. One Mass.

Surface density must exceed critical mass density somewherewithin the gravitational lens.

For multiple images, the object must lie within the cusp.

Ray Tracing: Multiple imagesRay Tracing: Multiple imagesCaustic cusp due to the gravitational lens is shown in ray tracing using the angle of deflection for individual rays in superposition.

Einstein Ring First complete ring observedHubble Telescope (1998)

Angular DeflectionAngular Deflection

Density Perturbations, Density Perturbations, Image to source mapping, Image to source mapping,

Time delay Time delay

R (Image) S (Source)

Time delay calculation is composed of the geometrical delay and the potential time delay

ReferencesReferences

Blandford, R., et al. Blandford, R., et al. Gravitational Lens Gravitational Lens Optics.Optics. .JSTOR. Science. 245: 824-830. 1989. Web. .JSTOR. Science. 245: 824-830. 1989. Web. Nov. 2010. Nov. 2010.

Bradac, M., et al. Bradac, M., et al. Revealing The Properties of Dark Revealing The Properties of Dark Matter in the Merging Cluster Macs J0025.4-1222Matter in the Merging Cluster Macs J0025.4-1222. . arXiv:0806.2320v2 [astro-ph]. 2008. Web. Nov. 2010.arXiv:0806.2320v2 [astro-ph]. 2008. Web. Nov. 2010.

Levine, H., A. Petters, J.Wambsganss. Levine, H., A. Petters, J.Wambsganss. Singularity Singularity Theory and Gravitational Lensing. Theory and Gravitational Lensing. Boston: Boston: Birkhauser, 2001.Birkhauser, 2001.

Mellier, Y., et al. Mellier, Y., et al. Lecture Notes in Physics: Lecture Notes in Physics: Gravitational lensing.Gravitational lensing. Berlin: Springer-Verlag, 1990. Berlin: Springer-Verlag, 1990.

ImagesImages King, L. U. Manchester. NICMOS ,HST, NASA. King, L. U. Manchester. NICMOS ,HST, NASA.

1998. 1998. http://apod.nasa.gov/apod/ap980330.htmlhttp://apod.nasa.gov/apod/ap980330.html Tsioulia, Andrew,. Gradient Index (GRIN) Lens. Tsioulia, Andrew,. Gradient Index (GRIN) Lens.

2003 2003 http://www.informaworld.com/smpp/contentnconthttp://www.informaworld.com/smpp/contentncontent=a713548186~db=all~dumptype=rssent=a713548186~db=all~dumptype=rss

Solar Eclipses Overview. 2010. Solar Eclipses Overview. 2010. http://scie.eja.int/science_e/www/object/index.cfhttp://scie.eja.int/science_e/www/object/index.cfm?fobjectid=37889&fbodylongid=1786m?fobjectid=37889&fbodylongid=1786

Grin Micro Lens. Grin Micro Lens. http://www.acphotonics.com/products/product_filhttp://www.acphotonics.com/products/product_files/GRIN%20/Lens.htmes/GRIN%20/Lens.htm

Optica Software. Optica Software. http://http://www.opticasoftware.com/faqswww.opticasoftware.com/faqs//