Practicable GLHUA Invisible Cloaks Absorb the Incident Wave and create Outgoing Wave Without Exceeding Light Speed Propagation and New N Dimensional Maxwell Equations

TL;DR

This paper introduces practical GLHUA invisible cloaks that absorb incident waves and generate outgoing waves without exceeding light speed, along with new analytical solutions and transformations for electromagnetic cloaking.

Contribution

The paper presents novel GLHUA cloaks with analytical EM wave solutions, new transformations, and a new ND Maxwell equation, advancing practical and theoretical aspects of electromagnetic invisibility.

Findings

GLHUA cloaks absorb incident waves and produce outgoing waves.

Analytical EM wave solutions are derived for the cloaks.

New ND Maxwell equations are formulated.

Abstract

In this paper, we propose practicable GLHUA invisible cloaks, our cloak absorb the incident wave and create outgoing wave that make them to be invisible cloaks and analytical electromagnetic (EM) wave without exceeding light speed propagation. Discoveries and creations are reported. 1. New GLHUA-i,i=1,2,3 annular layer EM invisible cloak with relative refractive index large or equal to 1. 2. Analytical EM wave solution of EM wave equation with the GLHUA 1-3 cloak materials are found, In GLHUA-1 cloak, $\varepsilon_r = \mu_r = \frac{{R_2 ^2 }}{{r^2 }}$, $\varepsilon_\theta = \varepsilon_\phi = \mu_\theta = \mu_\phi = \frac{{R_2 - R_1 }}{{r - R_1 }}$, In GLHUA-2 cloak, $\varepsilon _r = \mu _r = \frac{1}{{r^2 }}\frac{{(R_1 (r - R_1 ) + (R_2 - R_1 )^2 )^2 }}{{(R_2 - R_1 )^2 }}$,. 3. A GLHUA expansion method and an exact analytical EM wave propagation in the GLHUA-i,i=1,2,3 cloak without exceeding light speed propagation that are propsed. 4.Novel negative space is proposed. 5. GLHUANP-i, i=2,3 transformation are proposed, which maps $ - \infty $ to $R_1$ and $-R_2$ to $R_2$. 6. The GLHUANP-i, i=2,3 transformation creates GLHUA-2 and GLHUA-3 cloaks. 7. GLHUA-i, i=1,2,3 cloaks absorb the incident wave and create outgoing wave that make them invisible cloak and analytical EM wave through them. 8. GLHUAF transformation and .GLHUAF invisible cloak with double negative materials is created. 9. The relative parameters of the GLHUA-1 are large than 1, radial parameter in GLHUA-2 cloak is large than positive number, refractive index of the GLHUA 1-3 cloak are large than 1. 10. Two wave fronts in GLHUA cloaks one front is absorbing incoming incident, other front is created wave by cloak materials. 11. New ND Maxwell Eq. is created. The patent, copyright and all rights are reserved by authors in GLGEO in USA.