THE SOFT X-RAY AND EXTREME ULTRAVIOLET REGIONS OF THE ELECTROMAGNETIC SPECTRUM

One of the last regions of the electromagnetic spectrum to be developed is that between ultraviolet and x-ray radiation, generally shown as a dark region in charts of the spectrum. It is a region where there are a large number of atomic resonances, leading to absorption of radiation in very short distances, typically measured in nanometers (nm) or micrometers (microns, µm), in all materials. This has historically inhibited the pursuit and exploration of the region. On the other hand, these same resonances provide mechanisms for both elemental (C, N, O, etc.) and chemical (Si, SiO2, TiSi2) identification, creating opportunities for advances in both science and technology. Furthermore, because the wavelengths are relatively short, it becomes possible both to see smaller structures as in microscopy, and to write smaller patterns as in lithography. To exploit these opportunities requires advances in relevant technologies, for instance in materials science and nanofabrication. These in turn lead to new scientific understandings, perhaps through surface science, chemistry, and physics, providing feedback to the enabling technologies. Development of the extreme ultraviolet and soft x-ray spectral regions is presently in a period of rapid growth and interchange among science and technology. Figure 1.1 shows that portion of the electromagnetic spectrum extending from the infrared to the x-ray region, with wavelengths across the top and photon energies along the bottom.

In our studies of radiation from charged particles moving at velocities approaching that of light, a number of interesting phenomena are observed, such as the searchlight effect wherein radiation from the charged particle is constrained to a very narrow forward radiation cone. Furthermore, the calculation of detailed angular radiation patterns, in the frame of reference moving with the charged particle, and wavelength distributions are readily accomplished. The results can then be transformed back to the laboratory, or observer, frame of reference. For instance, the calculation of undulator radiation reduces to use of the well-known formula for so-called dipole radiation from a simple oscillating electron. With this approach we need solve Maxwell's equations for only the simplest radiating system, a small amplitude oscillating electron. This approach is not only simple to follow, but gives valuable physical insights to the radiation process and the parameters that characterize it.

In order to relate calculations in one frame of reference to those in another frame of reference when the relative speed between the two approaches that of light, we must make use of the Lorentz space-time transformations, which provide relationships between spatial and temporal scales in the two frames of reference, and are consistent both with Einstein's postulates of special relativity and with all known experiments (see Ref. 2 for a discussion of the Lorentz transformations and their reduction to Galilean transformations as v/c → 0).