Successive to the general application of terahertz and far-infrared spectroscopy to various kinds of subjects, properties of synchrotron radiation and the practical application of spectroscopy by synchrotron radiation in these regions are reviewed. Synchrotron radiation in these regions consists of incoherent and coherent components. In this article, the typical experimental subjects of which performance became feasible only by the application of incoherent synchrotron radiation are introduced. They are the change in phonon spectrum due to pressure-induced structural phase transition, far-infrared absorption-reflection spectroscopy, magnetic circular dichroism measurement, and microspectroscopy under high pressure. Finally, the perspective of spectroscopy in these regions based on the rapid development of the technology of the coherent synchrotron radiation is described.
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