[Paper Review] The Theoretical Proof for GLHUA EM Invisible Double Layer Cloak By Using GL No Scattering Modeling and Inversion

Jianhua Li, Feng Xie+2 more|arXiv (Cornell University)|Dec 31, 2016

Solar and Space Plasma Dynamics3 citations

TL;DR

This paper presents a theoretical proof for a GLHUA electromagnetic (EM) invisible double-layer cloak using GL no-scattering modeling and inversion, demonstrating that EM waves cannot penetrate into the concealed region due to phase velocity tending to zero at the inner boundary. The cloak uses relative permittivity and permeability parameters ≥1, ensuring subluminal wave propagation and perfect invisibility with no scattering, validated through rigorous mathematical theorems and analytical EM wave solutions.

ABSTRACT

In this paper, we proposed the GLHUA double layer cloak; proved the properties of GLHUA double layer cloak; Using GL no scattering inversion and the pre cloak condition 6.1 to 6.4 in paper [1], we create GLHUA outer layer cloak radial relative parameter and angular relative parameter theoretically. We proved theorem 4.1 to theorem 4.4 that the phase velocity of the electromagnetic wave in GLHUA outer layer cloak is less than light speed and tends to zero at the boundary $r=R_1$, the EM wave tends to zero at $r=R1$; When source $r_s > R_2$ in the outside of the cloak and observer $r_o < R_o$ in the concealment, then $\vec E(\vec r_o)=0$ and $\vec H(\vec r_o)=0$ that is proved in theorem 5.1 and 5.3. We prove that the EM wave excited in outside of the cloak can not propagation penetrate into the concealment. In theorem 5.4 to 5.6, we rigorously proved the EM wave excited in outside of the cloak can not be disturbed by the cloak. In theorem 6.1 to theorem 6.6, we prove that the EM wave excited in the concealment can not propagate to outside of GLHUA inner cloak. we prove that the EM wave excited in the concealment can not be disturbed by the cloak. We theoretically prove that the GLHUA double cloak is invisible cloak with concealment and with relative parameter not less than 1; the GLHUA double layer cloak is practicable. In December of 2016, we submitted 3 papers to arXiv for GLHUA double layer cloak with relative parameters not less than 1. This is the third paper. The task and content of the three paper are different from each other. The second paper [1] and this Paper are theoretical base and proof of the subjects in paper arXiv:1612.02857. We find an exact analytical EM wave field of Maxwell EM equation in GLHUA cloak and mirage bridge wave. Patent of the GLHUA EM cloaks,GLHUA sphere and GL modeling and inversion methods are reserved by authors in GL Geophysical Laboratory.

Motivation & Objective

• To theoretically prove the existence and invisibility of a double-layer electromagnetic cloak with relative parameters not less than 1.
• To establish a rigorous mathematical framework for EM wave behavior in anisotropic, inhomogeneous media using GL no-scattering inversion.
• To demonstrate that EM waves from external sources cannot penetrate into the concealed region due to phase velocity tending to zero at the inner boundary.
• To validate that the cloak does not scatter incident waves and that internal sources cannot radiate outward, ensuring full concealment.
• To provide a complete theoretical foundation for the GLHUA cloak as a practicable, non-singular, and physically realizable invisible cloak.

Proposed method

• Proposed a novel GLHUA outer layer cloak with radial and angular relative permittivity and permeability parameters derived via GL no-scattering inversion.
• Applied the pre-cloak conditions (6.1–6.4) from prior work to ensure continuity and non-singularity of EM parameters across boundaries.
• Introduced a new GL transform, $ r_p = R_1 + A e^{-B/r} $, to construct angular EM parameters in the outer cloak layer.
• Used generalized regularizing methods to analyze wave behavior near $ r = R_1 $, where phase velocity tends to zero.
• Formulated and solved the GL full-wave EM model using exact analytical solutions to the 3D Maxwell equations in spherical anisotropic media.
• Validated results via the GL EM Eikonal equation, showing discontinuous wave fronts and non-geometric ray propagation at $ r = R_1 $.

Experimental results

Research questions

• RQ1 Can a double-layer EM cloak with relative parameters ≥1 achieve perfect invisibility without exceeding light speed?
• RQ2 How does the phase velocity of EM waves behave as they approach the inner boundary $ r = R_1 $, and does it prevent wave penetration?
• RQ3 Can external EM sources excite detectable fields inside the concealed region $ r < R_1 $, or are the fields zero due to wave suppression?
• RQ4 Does the cloak scatter incident waves, and can internal sources radiate outward, violating the concealment principle?
• RQ5 Is there a rigorous analytical solution to the 3D Maxwell equations in the GLHUA cloak that confirms invisibility and subluminal propagation?

Key findings

• The phase velocity of EM waves in the GLHUA outer cloak is less than light speed and tends to zero as $ r \to R_1 $, preventing wave propagation into the concealed region.
• The electric and magnetic fields $ \vec{E}(\vec{r}_o) = 0 $ and $ \vec{H}(\vec{r}_o) = 0 $ at any observation point $ r_o < R_1 $, proving complete invisibility from external sources.
• External EM waves are not scattered by the cloak, as rigorously proven in Theorems 5.4–5.6, confirming no detectable interaction.
• Internal EM sources cannot excite outward-propagating waves, as shown in Theorems 6.1–6.6, ensuring concealment from outside observers.
• The GLHUA analytical EM wave solution for the 3D Maxwell equations confirms that no finite-time wave propagation reaches $ r = R_1 $, validating the cloak’s invisibility.
• The GLHUA mirage bridge effect—observed in simulations—further confirms non-luminal wave behavior and wavefront discontinuity at $ r = R_1 $, supporting the theoretical model.