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IEEE photonics journal

The Calculation and Analysis of the Bistatic Quantum Radar Cross Section for the Typical 2-D Plate

Chonghua Fang, Hui Tan, Qi-Feng Liu, Li Tao, Long Xiao, Yanjun Chen, Liang Hua

Published Mar 23, 2018• 44 citations
Publisher

Abstract

The quantum radar cross section (QRCS) describes how much return one gets when illuminating an object with a handful of photons. However, the previous studies mainly focused on the monostatic scattering of quantum radar. In this study, in response to the four key questions raised by ourselves in bistatic quantum radar cross section (BIQRCS), we calculate and analyze the BIQRCS for the typical tow-dimensional plate. First, as mentioned by Brandsema, the further derived analytical solution for the rectangular plate is obtained. In addition, the influence of incident frequency and the number of photons on the BIQRCS for the plate were obtained. Besides, we first reveal that the envelope curves of sidelobes in BIQRCS at the given incidence display the invariance in frequency. Finally, we show some comparison results among the BIQRCS, classical radar cross section (CRCS), and monostatic QRCS for the plate and find the advantage of sidelobe of the BIQRCS in given direction. We anticipate that these research results will find use in the detection and discrimination of stealthy platforms.

DOI
10.1109/jphot.2018.2818819

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Optics Express•May 2, 2022•7 citations
The quantum radar cross section (QRCS) describes how much return one gets when illuminating an object with a handful of photons. However, the previous studies mainly focused on the monostatic scattering of quantum radar. In this study, in response to the four key questions raised by ourselves in bistatic quantum radar cross section (BIQRCS), we calculate and analyze the BIQRCS for the typical tow-dimensional plate. First, as mentioned by Brandsema, the further derived analytical solution for the rectangular plate is obtained. In addition, the influence of incident frequency and the number of photons on the BIQRCS for the plate were obtained. Besides, we first reveal that the envelope curves of sidelobes in BIQRCS at the given incidence display the invariance in frequency. Finally, we show some comparison results among the BIQRCS, classical radar cross section (CRCS), and monostatic QRCS for the plate and find the advantage of sidelobe of the BIQRCS in given direction. We anticipate that these research results will find use in the detection and discrimination of stealthy platforms.
Closed-form expressions for the bistatic quantum radar scattered by the circular and triangular plates with the single-photon incidence are derived in the field of the Fourier relationship between the surface atom distribution and the bistatic quantum radar cross section (BIQRCS). The proposed expressions are highly efficient useful tools to analytically estimate the BIQRCS of the typical simple plates in the condition of high frequency approximation. And the formulas have been preliminarily verified by the numerical solution for the typical incident angles. In addition, the analysis of the quantum effect of sidelobes of BIQRCS in scattering, which can be seen as a kind of quantum interference, is also presented. We expect that this achievement will apply to the modeling of bistatic quantum radar scattering.
In radar, the amount of returns that an object sends back to the receiver after being struck by an electromagnetic wave is characterized by what is known as the radar cross section, denoted by � typically. There are many mechanisms that affect how much radiation is reflected back in the receiver direction, such as reflectivity, physical contours and dimensions, attenuation properties of the materials, projected cross sectional area and so on. All of these characteristics are lumped together in a single value of �, which has units of m2. Stealth aircrafts for example are designed to minimize its radar cross section and return the smallest amount of radiation possible in the receiver direction. A new concept has been introduced called quantum radar, that uses correlated quantum states of photons as well as the unique properties of quantum mechanics to ascertain information on a target at a distance. At the time of writing this dissertation, quantum radar is very much in its infancy. There still exist fundamental questions about the feasibility of its implementation, especially in the microwave spectrum. However, what has been theoretically determined, is that quantum radar has a fundamental advantage over classical radar in terms of resolution and returns in certain regimes. Analogous to the classical radar cross section (CRCS), the concept of the quantum radar cross section (QRCS) has been introduced. This quantity measures how “large” an object looks to a quantum radar be describing how a single photon, or small cluster of photons scatter off of a macroscopic target. Preliminary simulations of the basic quantum radar cross section equation have yielded promising results showing an advantage in sidelobe response in comparison to the classical RCS. This document expands upon this idea by providing insight as to where this advantage expanding upon the theory. The expanded theory presented in this document includes re-deriving the QRCS formula to be a general bistatic formula, as the current equation is only valid for monostatic radar geometries. This re-derivation process also leads to the addition of terms that capture the effect of photon polarization, something that is not properly taken into account in the current literature. Most importantly, a new formulation of the QRCS formula will be derived that includes writing the equation in terms of Fourier transforms. This has a profound impact on the analysis of the theory of the QRCS as it allows for the derivation of closed form solutions of certain geometries, something that has never been possible due to the form of the current QRCS equation. All together, this document will provide a complete and general theory of the QRCS. After deriving the necessary equations, there will be extensive work in the utilization of these equations in deriving geometry dependent responses and comparing the closed form solutions to the classical solutions as well as comparing the solutions to the numerical simulations. The current literature relies exclusively on numerical simulations…
A closed-form model of bistatic multiphoton quantum radar cross section (QRCS) for the cylindrical surface, the main structure of typical aircraft, especially missiles, is established to analyze the system and scattering characteristics. The influence of curvature of the three-dimensional target on QRCS is analyzed. By comparing and analyzing the bistatic multiphoton QRCS for a cylinder and a rectangular plate, we find that the QRCS for the convex surface target is the extension of the QRCS for the planar target with inhomogeneous atomic arrangement intervals and patterns. The characteristics of cylindrical QRCS are discussed by combining the transceiver system and the photon number of the transmitted signal, and the influences of the cylindrical radius, cylindrical length, and incident photon number on QRCS are analyzed. The bistatic results provide guidance on potential strong scattering directions for the target under various directions of photon incidence. Compared with the plane target, the cylindrical target amplifies scattering intensity near the target surface at the scattering angle side in the bistatic system. A bistatic multiphoton quantum radar system can achieve sharpening and amplification of the main lobe of the QRCS for a cylinder in an extensive scattering angle range. Bistatic multiphoton quantum radar has better visibility for the cylinder with a smaller length. These characteristics will provide prior information for research in many fields, such as photonic technology, radar technology, and precision metrology.
Quantum radar offers the prospect of detecting, identifying, and resolving RF stealth platforms and weapons systems, but the corresponding quantum radar cross section (QRCS) simulation is restricted-almost all existing methods can only be used for the two-dimensional (2-D) targets, not the 3-D targets even for convex targets. We propose a novel method that can deal with the calculation of the orthogonal projected area (A⊥) of the target in each incidence, which is the key part of QRCS simulation for the arbitrary 3-D convex target. To the best of our knowledge, this has not been reported before. In this paper, we introduce a three-step computation process of (A⊥), and verified the method for typical 2-D targets. Finally, we show some results for typical 3-D convex targets and compared the QRCS with classical radar cross section (CRCS). Meanwhile, we analyze the superposition of quantum effect of side lobes for 3-D convex targets. The proposed method provides a key improvement for realizing the universalization and utilization of QRCS calculation.
We derive a modified analytical expression of a quantum radar cross section (QRCS). Subsequently, we present a comparison between the QRCS and a classical radar cross section (RCS) and analyze the factors that can affect the intensity of the peak and side lobes. Simulation results on a flat rectangular plate demonstrate that QRCS has a similar structure to that of RCS. The analysis of side-lobe structure can benefit the design of quantum stealth platforms as well as the research on quantum radars.
A closed-form model of multiphoton quantum radar cross-section (QRCS) in the monostatic scenes is constructed for rectangular flat plates based on quantum interference and uncertainty. The model is justified by the comprehensive analysis of the model parameters in the model building process. Then, we use the model to quantitatively analyze the main lobe enhancement effect of multiphoton QRCS, which means that the more incident photons will enhance the main lobe magnitude of QRCS with other factors being the same. Moreover, we predict that enhancement effects might also exist for the side lobe close to the main lobe. In addition, we present the specific conditions for side lobe enhancement. On this basis, the enhancement angle range is defined to unify the description of the main lobe and side lobe enhancement effects. The influencing factors of the enhancement angle range are clarified. The results exhibit that the angle range of enhancement in multiphoton QRCS fluctuates with the change of target size and incident wavelength. All enhancement effects are exponentially related to the incident photon number. This work brings the description of multiphoton QRCS into the closed-form model analysis stage, which will provide prior information for research in many fields, such as photonic technology, radar technology, and precision metrology.