<title>Near-field computation methods</title>

Abstract

The advance of nanotechnologies in electronics and optics has offered possibilities of applying methods of near-field optics. Optical memory is the area where these methods can be successfully employed. It is now possible to make memory elements with the bit size as small as a few tens of nanometers (which corresponds to the storage density of 1011 bit/cm). Nanoelectronics methods and synthesized hologram techniques can also be used for this purpose. With such small bit size data reading becomes rather a problem. Based on the wave optics principles, the wavelength of the reading laser should be of the order of bit size. Though the wavelengths of diode lasers now approach 400 nm (there are already blue diode lasers with ?.=4O4 mu), wavelengths shorter than 390 nm are hardly possible in the near future. It means that the bit size is always smaller than the wavelength of diode lasers. To overcome this difficulty, we should apply the superresolution approach, which is realized in near-field optics. Another important field of application of near-field optics is scanning optical microscopy, especially noncontact microscopy of subnanometer resolution. The development of such microscopes may be important not only for making optical data storage systems but also for investigating biological structures. In this regard, the analysis of possible approaches to near-field calculations of electromagnetic field assumes great significance. It should be noted that the near-field theory is well elaborated and found practical use The mathematics of the theory based on Huygens's principle and Kirchhoff's formula is successfully used for studying different diffraction phenomena. However, though applicable in a number of approximations, this mathematics does not work in the near-field calculations (especially when R is of the order of 2). This brings up the questions: how can the field be determined in this case, can we apply Kirchhoff's formula and Huygens's construction, or should we employ Maxwell equations and solve a boundary problem for each particular case. There are other, more subtle, questions (especially when R is ofthe order of)t) involving coherence and interference effects, wave formation, etc. We start the analysis with the approximations that are used in the deduction of Kirchhoff's formula, then proceed with rigorous mathematical treatment of Huygens's construction, and conclude with the consideration of field properties near the light source when R<'(A..