Optics in hyperbolic space
نویسندگان
چکیده
منابع مشابه
Hamiltonian Optics of Hyperbolic Polaritons in Nanogranules.
Semiclassical quantization rules and numerical calculations are applied to study polariton modes of materials whose permittivity tensor has principal values of opposite sign (so-called hyperbolic materials). The spectra of volume- and surface-confined polaritons are computed for spheroidal nanogranules of hexagonal boron nitride, a natural hyperbolic crystal. The field distribution created by p...
متن کاملComplex Geometric Optics for Symmetric Hyperbolic Systems Ii: Nonlinear Theory in One Space Dimension
This is the second part of a work aimed to study complex-phase oscillatory solutions of nonlinear symmetric hyperbolic systems. We consider, in particular, the case of one space dimension. That is a remarkable case, since one can always satisfy the naive coherence condition on the complex phases, which is required in the construction of the approximate solution. Formally the theory applies also...
متن کاملHyperbolic Space
Radial lines, suitably parameterized, are geodesics, but notice that the distance from the origin to the (Euclidean) unit sphere is infinite. This model makes it intuitively clear that the boundary at infinity of hyperbolic space is Sn−1. Hyperbolic space together with its boundary at infinity has the topology of a closed ball, and isometries of hyperbolic space extend uniquely to a homeomorphi...
متن کاملHyperbolic Partial Differential Equations and Geometric Optics
§1.1. The method of characteristics §1.2. Examples of propagation of singularities using progressing waves §1.3. Group velocity and the method of nonstationary phase §1.4. Fourier synthesis and rectilinear propagation §1.5. A cautionary example in geometric optics §1.6. The law of reflection §1.6.1. The method of images §1.6.2. The plane wave derivation §1.6.3. Reflected high frequency wave pac...
متن کاملUniversal Approximator Property of the Space of Hyperbolic Tangent Functions
In this paper, first the space of hyperbolic tangent functions is introduced and then the universal approximator property of this space is proved. In fact, by using this space, any nonlinear continuous function can be uniformly approximated with any degree of accuracy. Also, as an application, this space of functions is utilized to design feedback control for a nonlinear dynamical system.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1928
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1928-1501420-5