Abstract-The scattering characteristic of paraxial gaussian beam from two dimensional dielectric rough surfaces is studied in this paper. The modification of the Kirchhoff approximation theory for rough surface scattering by an incident gaussian beam instead of a plane wave are developed based on conventional Kirchhoff scattering theory and plane wave spectrum expansion method. The coherent and incoherent scattered intensity and cross section of two dimensional dielectric rough surfaces is derived in detail. As a application, under incidence wave length λ = 1.06 µm, we calculate the coherent and incoherent scattered intensity and cross section of Gaussian beam scattering from plating aluminium dielectric rough surfaces change with the scattering zenith angles in different rough surface correlation length, rough surface height root mean square and other conditions. In the same scattering conditions, we compare the coherent and incoherent scattered section between the gaussian beam and plane wave to prove that our methods and programming cods is correct. The numerical results are shown 224 Wang, Wu, and Li that the incident gaussian beam size is much larger compared with the surface height correlation length, the normalized scattering cross section is the same as for an incident plane wave. The ratio between the beam size and the surface height correlation length play an important role in the scattering characteristic of the gaussian beam from two dimensional dielectric rough surfaces. The ratio is bigger, the coherent and scattered intensity and section is more remarkable and on the contrary the incoherent scattered intensity and section is relatively smaller.

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The reflection and transmission of an incident Gaussian beam by a uniaxial anisotropic slab are investigated, by expanding the incident Gaussian beam, reflected beam, internal beam as well as transmitted beam in terms of cylindrical vector wave functions. The unknown expansion coefficients are determined by virtue of the boundary conditions. For a localized beam model, numerical results are provided for the normalized field intensity distributions, and the propagation characteristics are discussed concisely.

Abstract-Obtaining scattering field for an ellipsoid irradiated by electromagnetic wave with arbitrary polarizing and propagating direction is a hard topic that has caused large attention in the world. Literatures relative to it are seldom found. In this paper, the scattering field for an ellipsoid is presented by utilizing the scales transformation of electromagnetic field and coordinate system rotation, as the incident wave irradiating the target with arbitrary polarizing and propagating direction. The result obtained is in good agreement with that in the reference when all the scale factors changes into 1. We take a conductor ellipsoid as an example, simulations both for ellipsoid and plant leaf are presented respectively by way of choosing the different scale factor. Results show that the scattering field is sensitively affected by polarization of the incident wave and varies not too greatly with the incident wave and changes with the observing point. At some points the scattering energy arrives to its maximum.

This paper proposes a systematic analysis method for 5G Non-Access Stratum Signalling security based on formal analysis, which has identified 10 new 5G protocol vulnerabilities, and an improved PKI security mechanism targeted at eliminating these vulnerabilities. Firstly, the 5G system, state transition properties and security properties were abstracted from 3GPP specifications. To mimic an attacker's behavior, a Dolev-Yao adversary model was constructed in the 5G model by empowering it with NAS signalling security testing knowledge and reasonable security capabilities in the wireless channel. Then we used the TAMARIN prover to verify all the abstracted properties one by one and discovered some protocol vulnerabilities based on the counterexamples found. We further verified these vulnerabilities on the testbed and identified 10 new 5G protocol vulnerabilities. Moreover, we analyzed the root cause of these vulnerabilities and concluded that all of them were caused by the unconditional trust between UE and gNodeB. Therefore, we propose an improved PKI mechanism based on the existing asymmetric encryption of 5G. Besides the existing public-private key pair of the home network, we introduce a new pair of asymmetric keys in the gNodeB to encrypt and sign the signalling message sent to UE. The gNodeB can be connected only when the verification succeeds and then the RRC connection can be initiated. This mechanism can effectively avoid all the vulnerabilities found in this paper. INDEX TERMS 5G, protocol security, privacy, NAS, formal method, public key infrastructure.