This book deals with a recently developed theoretical method for calculating the optical response of nanoscale or mesoscopic matter. There has been much interest in this type of matter system because it brings out a new feature of solid state physics, viz. , the central importance of the quantum mechanical coherence of matter in its transport and optical properties, in contrast to bulk systems. The author has been interested in the optical properies of mesoscopic matter since the mid-1980s, seeking to construct a new theoretical framework beyond the traditional macroscopic optical response theory. The new element to be included is the microscopic spatial structure of the response field and induced polarization, and the nonlocal relationship between them. This is the counterpart of the size quantization of confined electrons or excitons reflecting the sampIe size and shape in detail. AIthough the latter aspect has been widely discussed, the former has not received due attention, and this has prompted the author to introduce a new theoretical framework. This book describes such a theory, as developed by the author's present group. Although it is only one of several such frameworks, we believe that it is constructed in a sufficiently general manner to apply to the study of the linear and nonlinear optical responses of nanostructures of various sizes and shapes, subjects of considerable interest today.

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This book gives a theoretical description of linear and nonlinear optical responses of matter with special emphasis on the microscopic and "nonlocal" nature of resonant response. The response field and induced polarization are determined self-consistently in terms of simultaneous linear or nonlinear polynomial equations. This scheme is a general one with its position between QED and macroscopic response theory, but is most appropriate for determining the dependence of optical signals on the size, shape, and internal structure of a nanostructure sample. As a highlight of the scheme, the multi-resonant enhancement of the DFWM signal is described together with its experimental verification.

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