Research IdeasFractal Zone Plates and Photon SievesFractal zone plates are a special type of zone plate where the pattern of the zones is fractal. As a result, there is a certain degree of fractal structure in the foci that is characteristic of the fractal zone plate. The fractal design can also be used the modify both the number and the relative intensities of the foci, something that may prove very useful for imaging. Similarly, photon sieves can be constructed with a fractal pattern and this also provides some advantages. While the fractal photon sieve focuses light at the first focus similarly to a fractal zone plate, the photon sieve also suppresses higher order focal points, leading to much clearer, if dimmer, image. The fractal photon sieve also has all of the advantages over the fractal zone plate that the normal photon sieve has over the normal zone plate. Links:
Photon SievesPhoton Sieves are very similar to zone plates in both their function and their design, but address several issues with zone plates. First of all, zone plates produce secondary maxima that show up as rings around the focus. These rings reduce the quality of the image and can be very problematic in the realm of precision optics. Photon Sieves are similar to zone plates, but instead of rings, they are composed of many, many pinholes arranged in the same pattern as the rings of a zone plate. By not including each full ring, however, the photon sieve is actually able to suppress the secondary maxima that are apparent in zone plate images. As a result, photon sieves are actually much more useful in soft x-ray focusing than are zone plates. It would be interesting to see how photon sieves would work for imaging, where light is not monochromatic, so there will be aberrations that result from the different wavelengths. Like I proposed for zone plates, these aberrations might be correctable through the use of a filter that bends different wavelengths of light differently. Hopefully this will be able to correct the image and bring the different focal points closer together. Photon sieves also have an advantage over zone plates bacause their openings are not confined by the size of the fresnel zones. The pinholes that compose the photon sieves can actually be slightly larger than their corresponding zones. Since the resolution of the image formed does not depend on the size of the pinhole itself, but instead on the size of the zone it is positioned in, the resolution of an image formed by a photon sieve can actually be much better than the resolution of the fabrication process used to make it (assuming that the hole is placed precisely). Photon sieves, however, do have one major drawback. Because they have less area for light to pass through, the intensity of light at the primary focus will be less than that of a zone plate. A zone plate transmits 50% of incident light, while a photon sieve transmits only about 15-20% of incident light. Because the Intensity scales with the square of the area, a zone plate will have a primary focus that is approximately ten times brighter than the corresponding zone plate. This is a tremendous drawback for any type of imaging and would require extremely long exposure times. Links:
Fresnel Zone PlatesZone Plates are diffraction patterns that were discovered by Augustin-Jean Fresnel and have very unique properties. Normally, light is focused by the use of lenses which bend (refract) light by changing the speed of the wave. Zone plates do the same thing but use diffraction instead. Waves passing through a zone plate cancel out will other and the end result is that the light constructively interferes at the focal point and destructively interferes in other places. Thus, a zone plate can actually be used in much the same way as a lens, but is much cheaper to manufacture and transport. Because they can focus any type of light, zone plates are very used very frequently in x-ray optics, where glass can no longer bend the light easily. As a result, it is extremely expensive to find materials that focus x-rays and then to manufacture those materials. Zone plates significantly reduce these costs. Zone plates are also being looked at for use in astronomy. Currently, some of the biggest costs associated with space-based telescopes are the costs of lifting the object into space. Glass plays a major factor here, since the mirrors used to focus the light are some of the heaviest components. In addition, zone plates have the advantage of being easy to fabricate with extreme precision, while the very precise mirrors that are currently used are extremely expensive. For all their benefits, zone plates have some disadvantages. First of all, zone plates will focus different wavelengths of light at different points, leading to aberrations when taking general images. While lenses do the same thing, the difference between wavelengths is much less pronounced. Also, zone plates, by their nature, block out 50% of the light that hits them, and even more light is lost in practice. As a result, they are not very efficient and any imaging done with zone plates will take twice as long as with lenses/mirrors. Although not perfect, zone plates have tremendous potential to significantly improve optics and imaging especially in the fields of astronomy and lasers. Project Ideas:
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MetamaterialsMetamaterials are a new type of materials that have been designed and fabricated by scientists to have very special properties that previously were thought to be impossible. One of the most important properties of a metamaterial is a negative index of refraction. What this means that light will be refracted when entering a new material in such a way that the refracted ray will be on the same side of the normal as the incident ray. Another interesting property of metamaterials is that they effectively reverse the Doppler Shift; a light source moving towards an observer appears redshifted and a light source moving away appears blueshifted. Additionally, metamaterials may also be able to construct so called perfect lenses that can image object smaller than the wavelength of the light being used. Using metamaterials optics may no be diffraction limited but may instead only be limited by the fabrication technology. One of the most important and promising uses for metamaterials is their ability to effectively cloak a region of space by bending the light around it so that there is no scattering and the light is reformed on the other side of the cloaked region. In this way, the light will be completely undisturbed and materials could potentially be made invisible. Links:
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