Beginning Ideas

Gravitational Lensing:

The deflection of a light source from sources more distant than the lens depends on the gravitational potential, independent of luminous or dark matter.

Gravitational lensing can be split up into three types:

Strong lensing - this is the extreme bending of light when a lens is very massive causing light to take different paths causing multiple (magnified and distorted) images

Weak lensing - occurs when the alignment between observer, lens and source is not close therefore slightly distorted images appear

Microlensing - the lensing is so small or faint one doesn't see the multiple images, the source may just appear brighter

There is deflection due to gravitational lensing. It depends upon the mass distribution of the lens which is calculated by GR; the bend angle depends on the gradient of the deflection potential. The extended mass distribution can figure out the deflection (treat as a collection of point masses). The location of the images will depend on the deflection angle, which in turn depends on mass distribution or deflection potential of the lens.

Geometric optics:

Geometric optics provides rules, which may depend on the color(wavelength) of the ray, for propagating these rays through an optical system. It fails to account for optical effects of diffration and interference. However, it makes an excellent approximation when the wavelength is very small compared to the size of structures with which the light interacts.

It's used to describe imaging, including optical aberrations. Optical aberrations occur when light from one point of an object does not converge into (or does not diverge from) a single point after transmission through the system. Aberration leads to blurring of the image produced by an image-forming optical system (makers of optical instruments need to correct optical systems to compensate for aberration).


A caustic is the envelope of light rays reflected or refracted by a curved surface of a object, or the projection of that envelope of rays on another surface. Caustics can be patches of light or their bright edges - shapes often have cusp singularities.

Example: A rainbow is a caustic. The scattering of light by raindrops causes different wavelengths of light to be reflected into arcs of differeing radius producing the bow.

Topological defects:

Topological defects are stable configurations of matter formed at phase transitions in the very early Universe. These configurations are in the original, symmetric or old phase, but nevertheless they persist after a phase transition to the asymmetric or new phase is completed. Topological defects(or disclination) may be formed when a symmetry is broken into a phase transition.

Topological defects carry energy; energy leads to an attractive gravitational force. Therefore, defects can act as seeds for cosmic structures such as cosmic strings and global textures, which can lead to attractive scenarios for formation of galaxies and large-scale structure.

In "new cosmology" matter is described in terms of fields. This leads to the posibility of having phase transitions in the early Universe where topological defects are formed and could have played a role in structure formation.

In liquid crystals, defects arise during the transition from disordered phase to the ordered phase. Recently there have been some ingenious studies of dynamics of defect formation in liquid crystals.

Liquid Crystal Lasers:

Liquid crystals are everywhere, from moblie telephones to high-definition flat-panel displays. These technologies are based on the reorientation of liquid-crystal material in response to applied electric fields, which result in a change in the observed optical properties. The majority of commercial displays are based on liquid crystals exhibiting a nematic phase.

Now, liquid crystals are being revolutionized in a whole different field, that of tunable organic lasers. The key feature that these materials possess is the exstence of photonic bandgap for visible light. Photonic band structures have attracted considerable attention because of their ability to control the propagation of light at a range of different frequencies.

One of the main advantages of using liquid crystals over photonic crystals is that their periodic structure forms spontaneously without the need for complex fabrication procedures, and that such soft matter may be readily deformed to achieve easy wavelength tuning.

Caustic Images:

Caustic Images are controled caustic patterns that can form almost any desired shape by optimizing the geometry of the reflective or refractive surface generating the caustic.