Dielectric permittivity Peter Hertel Overview Maxwell's Dielectric permittivity equations Definition Kramers- Kronig Peter Hertel Relation Onsager Relation University of Osnabr¨uck,Germany Summary Lecture presented at Nankai University, China http://www.home.uni-osnabrueck.de/phertel October/November 2011 Dielectric permittivity Peter Hertel Overview Maxwell's equations Definition Kramers- Kronig Relation Onsager Relation Summary Make it as simple as possible, but not simpler • Optics deals with the interaction of light with matter. • Light, as an electromagnetic field, obeys Maxwell's equations. • The Lorentz force on charged particles describes the interaction of light with matter. • We recapitulate Maxwell's equation in the presence of matter and specialize to a homogeneous non-magnetic linear medium. • We formulate the retarded response of matter to a perturbation by an electric field • It is described by the frequency-dependent susceptibility • The real part and the imaginary part of the susceptibility are intimately related. • If properly generalized to anisotropic media, the susceptibility is a symmetric tensor, provided an exteral magnetic field is reversed. Dielectric permittivity Peter Hertel Overview Overview Maxwell's equations Definition Kramers- Kronig Relation Onsager Relation Summary • Light, as an electromagnetic field, obeys Maxwell's equations. • The Lorentz force on charged particles describes the interaction of light with matter. • We recapitulate Maxwell's equation in the presence of matter and specialize to a homogeneous non-magnetic linear medium. • We formulate the retarded response of matter to a perturbation by an electric field • It is described by the frequency-dependent susceptibility • The real part and the imaginary part of the susceptibility are intimately related. • If properly generalized to anisotropic media, the susceptibility is a symmetric tensor, provided an exteral magnetic field is reversed. Dielectric permittivity Peter Hertel Overview Overview • Optics deals with the interaction of light with matter. Maxwell's equations Definition Kramers- Kronig Relation Onsager Relation Summary • The Lorentz force on charged particles describes the interaction of light with matter. • We recapitulate Maxwell's equation in the presence of matter and specialize to a homogeneous non-magnetic linear medium. • We formulate the retarded response of matter to a perturbation by an electric field • It is described by the frequency-dependent susceptibility • The real part and the imaginary part of the susceptibility are intimately related. • If properly generalized to anisotropic media, the susceptibility is a symmetric tensor, provided an exteral magnetic field is reversed. Dielectric permittivity Peter Hertel Overview Overview • Optics deals with the interaction of light with matter. Maxwell's • Light, as an electromagnetic field, obeys Maxwell's equations equations. Definition Kramers- Kronig Relation Onsager Relation Summary • We recapitulate Maxwell's equation in the presence of matter and specialize to a homogeneous non-magnetic linear medium. • We formulate the retarded response of matter to a perturbation by an electric field • It is described by the frequency-dependent susceptibility • The real part and the imaginary part of the susceptibility are intimately related. • If properly generalized to anisotropic media, the susceptibility is a symmetric tensor, provided an exteral magnetic field is reversed. Dielectric permittivity Peter Hertel Overview Overview • Optics deals with the interaction of light with matter. Maxwell's • Light, as an electromagnetic field, obeys Maxwell's equations equations. Definition Kramers- • The Lorentz force on charged particles describes the Kronig Relation interaction of light with matter. Onsager Relation Summary • We formulate the retarded response of matter to a perturbation by an electric field • It is described by the frequency-dependent susceptibility • The real part and the imaginary part of the susceptibility are intimately related. • If properly generalized to anisotropic media, the susceptibility is a symmetric tensor, provided an exteral magnetic field is reversed. Dielectric permittivity Peter Hertel Overview Overview • Optics deals with the interaction of light with matter. Maxwell's • Light, as an electromagnetic field, obeys Maxwell's equations equations. Definition Kramers- • The Lorentz force on charged particles describes the Kronig Relation interaction of light with matter. Onsager • We recapitulate Maxwell's equation in the presence of Relation matter and specialize to a homogeneous non-magnetic Summary linear medium. • It is described by the frequency-dependent susceptibility • The real part and the imaginary part of the susceptibility are intimately related. • If properly generalized to anisotropic media, the susceptibility is a symmetric tensor, provided an exteral magnetic field is reversed. Dielectric permittivity Peter Hertel Overview Overview • Optics deals with the interaction of light with matter. Maxwell's • Light, as an electromagnetic field, obeys Maxwell's equations equations. Definition Kramers- • The Lorentz force on charged particles describes the Kronig Relation interaction of light with matter. Onsager • We recapitulate Maxwell's equation in the presence of Relation matter and specialize to a homogeneous non-magnetic Summary linear medium. • We formulate the retarded response of matter to a perturbation by an electric field • The real part and the imaginary part of the susceptibility are intimately related. • If properly generalized to anisotropic media, the susceptibility is a symmetric tensor, provided an exteral magnetic field is reversed. Dielectric permittivity Peter Hertel Overview Overview • Optics deals with the interaction of light with matter. Maxwell's • Light, as an electromagnetic field, obeys Maxwell's equations equations. Definition Kramers- • The Lorentz force on charged particles describes the Kronig Relation interaction of light with matter. Onsager • We recapitulate Maxwell's equation in the presence of Relation matter and specialize to a homogeneous non-magnetic Summary linear medium. • We formulate the retarded response of matter to a perturbation by an electric field • It is described by the frequency-dependent susceptibility • If properly generalized to anisotropic media, the susceptibility is a symmetric tensor, provided an exteral magnetic field is reversed. Dielectric permittivity Peter Hertel Overview Overview • Optics deals with the interaction of light with matter. Maxwell's • Light, as an electromagnetic field, obeys Maxwell's equations equations. Definition Kramers- • The Lorentz force on charged particles describes the Kronig Relation interaction of light with matter. Onsager • We recapitulate Maxwell's equation in the presence of Relation matter and specialize to a homogeneous non-magnetic Summary linear medium. • We formulate the retarded response of matter to a perturbation by an electric field • It is described by the frequency-dependent susceptibility • The real part and the imaginary part of the susceptibility are intimately related. Dielectric permittivity Peter Hertel Overview Overview • Optics deals with the interaction of light with matter. Maxwell's • Light, as an electromagnetic field, obeys Maxwell's equations equations. Definition Kramers- • The Lorentz force on charged particles describes the Kronig Relation interaction of light with matter. Onsager • We recapitulate Maxwell's equation in the presence of Relation matter and specialize to a homogeneous non-magnetic Summary linear medium. • We formulate the retarded response of matter to a perturbation by an electric field • It is described by the frequency-dependent susceptibility • The real part and the imaginary part of the susceptibility are intimately related. • If properly generalized to anisotropic media, the susceptibility is a symmetric tensor, provided an exteral magnetic field is reversed. 1 0r · E = % 2 r · B = 0 3 r × E = −∇t B 4 (1/µ0)r × B = 0 rt E + j The electromagnetic field E and B accelerates charged particles p_ = qfE(t; x) + v × B(t; x)g At time t, the particle is at x, has velocity v = x_ and momentum p. Its electric charge is q. Dielectric permittivity Peter Hertel Maxwell's equations Overview Maxwell's equations Definition Kramers- Kronig Relation Onsager Relation Summary 1 0r · E = % 2 r · B = 0 3 r × E = −∇t B 4 (1/µ0)r × B = 0 rt E + j p_ = qfE(t; x) + v × B(t; x)g At time t, the particle is at x, has velocity v = x_ and momentum p. Its electric charge is q. Dielectric permittivity Peter Hertel Maxwell's equations Overview Maxwell's equations The electromagnetic field E and B accelerates charged Definition particles Kramers- Kronig Relation Onsager Relation Summary 1 0r · E = % 2 r · B = 0 3 r × E = −∇t B 4 (1/µ0)r × B = 0 rt E + j At time t, the particle is at x, has velocity v = x_ and momentum p. Its electric charge is q. Dielectric permittivity Peter Hertel Maxwell's equations Overview Maxwell's equations The electromagnetic field E and B accelerates charged Definition particles Kramers- Kronig Relation p_ = qfE(t; x) + v × B(t; x)g Onsager Relation Summary 1 0r · E = % 2 r · B = 0 3 r × E = −∇t B 4 (1/µ0)r × B = 0 rt E + j Dielectric permittivity Peter Hertel Maxwell's equations Overview Maxwell's equations The electromagnetic field E and B accelerates charged Definition particles Kramers- Kronig Relation p_ = qfE(t; x) + v × B(t; x)g Onsager Relation At time t, the particle is at x, has velocity v = x_ and Summary momentum p. Its electric charge