Two concepts of phenomenological optics of homogeneous, anisotropic and dispersive media are compared, the younger and more general concept of media with spatial dispersion and the older concept of (bi)-anisotropic me...Two concepts of phenomenological optics of homogeneous, anisotropic and dispersive media are compared, the younger and more general concept of media with spatial dispersion and the older concept of (bi)-anisotropic media with material tensors for electric and magnetic induction which only depend on the frequency. The general algebraic form of the polarization vectors for the electric field and their one-dimensional projection operators is discussed without the degenerate cases of optic axis for which they become two-dimensional projection operators. Group velocity and diffraction coefficients in an approximate equation for the slowly varying amplitudes of beam solutions are calculated. As special case a polariton permittivity for isotropic media with frequency dispersion but without losses is discussed for the usual passive case and for the active case (occupation inversion of two energy levels that goes in direction of laser theory) and the group velocity is calculated. For this active case, regions of frequency and wave vector with group velocities greater than that of light in vacuum were found. This is not fully understood and due to large diffraction is likely only to realize in guided resonator form. The notion of “negative refraction” is shortly discussed but we did not find agreement with its assessment in the original paper.展开更多
We consider the tensor product π_α ? π_βof complementary series representations π_α and π_β of classical rank one groups SO_0(n, 1), SU(n, 1) and Sp(n, 1). We prove that there is a discrete component π_(α+β...We consider the tensor product π_α ? π_βof complementary series representations π_α and π_β of classical rank one groups SO_0(n, 1), SU(n, 1) and Sp(n, 1). We prove that there is a discrete component π_(α+β)for small parameters α and β(in our parametrization). We prove further that for SO_0(n, 1) there are finitely many complementary series of the form π_(α+β+2j,)j = 0, 1,..., k, appearing in the tensor product π_α ? π_βof two complementary series π_α and π_β, where k = k(α, β, n) depends on α, β and n.展开更多
文摘Two concepts of phenomenological optics of homogeneous, anisotropic and dispersive media are compared, the younger and more general concept of media with spatial dispersion and the older concept of (bi)-anisotropic media with material tensors for electric and magnetic induction which only depend on the frequency. The general algebraic form of the polarization vectors for the electric field and their one-dimensional projection operators is discussed without the degenerate cases of optic axis for which they become two-dimensional projection operators. Group velocity and diffraction coefficients in an approximate equation for the slowly varying amplitudes of beam solutions are calculated. As special case a polariton permittivity for isotropic media with frequency dispersion but without losses is discussed for the usual passive case and for the active case (occupation inversion of two energy levels that goes in direction of laser theory) and the group velocity is calculated. For this active case, regions of frequency and wave vector with group velocities greater than that of light in vacuum were found. This is not fully understood and due to large diffraction is likely only to realize in guided resonator form. The notion of “negative refraction” is shortly discussed but we did not find agreement with its assessment in the original paper.
文摘We consider the tensor product π_α ? π_βof complementary series representations π_α and π_β of classical rank one groups SO_0(n, 1), SU(n, 1) and Sp(n, 1). We prove that there is a discrete component π_(α+β)for small parameters α and β(in our parametrization). We prove further that for SO_0(n, 1) there are finitely many complementary series of the form π_(α+β+2j,)j = 0, 1,..., k, appearing in the tensor product π_α ? π_βof two complementary series π_α and π_β, where k = k(α, β, n) depends on α, β and n.
