Throughout my whole career including student time I have had a feeling that leaning and teaching electromagnetism, especially macroscopic Maxwell equations (M-eqs) is dif?cult. In order to make a good use of these equations, it seemed necessary to be able to use certain empirical knowledges and model-dependent concepts, rather than pure logics. Many of my friends, colleagues and the physicists I have met on various occasions have expressed similar impressions. This is not the case with microscopic M-eqs and quantum mechanics, which do not make us feel reluctant to teach, probably because of the clear logical structure. What makes us hesitate to teach is probably because we have to explain what we ourselves do not completely understand. Logic is an essential element in physics, as well as in mathematics, so that it does not matter for physicists to experience dif?culties at the initial phase, as far as the logical structure is clear. As the we- known principles of physics say, "a good theory should be logically consistent and explain relevant experiments." Our feeling about macroscopic M-eqs may be related with some incompleteness of their logical structure.

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 situated 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.

This book discusses the electromagnetic response function of matter, providing a logically more complete form of macroscopic Maxwell equations than the conventional literature. It shows that various problems inherent to the conventional macroscopic Maxwell equations are solved by the first-principles derivation presented. Applying long wavelength approximation to microscopic nonlocal response theory results in only one susceptibility tensor covering all the electric, magnetic and chiral polarizations, and the book provides its quantum mechanical expression in terms of the transition energies of matter and the lower moments of corresponding current density matrix elements. The conventional theory in terms of epsilon and mu is recovered in the absence of chirality under the condition that magnetic susceptibility is defined with respect to not H, but to B. This new edition includes discussions supporting the basis of the present electromagnetic response theory in a weakly relativistic regime, showing the gauge invariance of many-body Schroedinger equation with explicit Coulomb potential, the relationship between this theory and the emergent electromagnetism, and the choice of appropriate forms of single susceptibility theory and chiral constitutive equations.

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. It will have a tremendous influence on modern device techniques, as it deals with frontier research in response theory.