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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Quantum computation of the electromagnetic cross section of dielectric targets

Marco O. Lanzagorta, Jeffrey K. Uhlmann, Oliverio Jitrik, Salvador Elías Venegas-Andraca, Seth Wiesman

Published May 12, 2016• 2 citations
Publisher

Abstract

The Radar Cross Section (RCS) is a crucial element for assessing target visibility and target characterization, and it depends not only on the target’s geometry but also on its composition. However, the calculation of the RCS is a challenging task due to the mathematical description of electromagnetic phenomena as well as the computational resources needed. In this paper, we will introduce two ideas for the use of quantum information processing techniques to calculate the RCS of dielectric targets. The first is to use toolboxes of quantum functions to determine the geometric component of the RCS. The second idea is to use quantum walks, expressed in terms of scattering processes, to model radar absorbing materials.

DOI
10.1117/12.2224078

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The Radar Cross Section (RCS) is a crucial element for assessing target visibility and target characterization, and it depends not only on the target’s geometry but also on its composition. However, the calculation of the RCS is a challenging task due to the mathematical description of electromagnetic phenomena as well as the computational resources needed. In this paper, we will introduce two ideas for the use of quantum information processing techniques to calculate the RCS of dielectric targets. The first is to use toolboxes of quantum functions to determine the geometric component of the RCS. The second idea is to use quantum walks, expressed in terms of scattering processes, to model radar absorbing materials.
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…
It has been found that the quantum radar cross section (QRCS) equation can be written in terms of the Fourier transform of the surface atom distribution of the object. This paper uses this form to provide an analytical formulation of the quantum radar cross section by deriving closed form expressions for various geometries. These expressions are compared to the classical radar cross section (RCS) expressions and the quantum advantages are discerned from the differences in the equations. Multiphoton illumination is also briefly discussed.
The radar cross section σC is an objective measure of the "radar visibility" of an object. As such, σC is an important concept for the correct characterization of the operational performance of radar systems. Furthermore, σC is equally essential for the design and development of stealth weapon systems and platforms. Recent years have seen the theoretical development of quantum radars, that is, radars that operate with a small number of photons. In this regime, the radar-target interaction is described through photon-atom scattering processes governed by the laws of quantum electrodynamics. As such, it is theoretically inconsistent to use the same σC to characterize the performance of a quantum radar. In this paper we define a quantum radar cross section σQ based on quantum electrodynamics and interferometric considerations. We discuss the theoretical challenges of defining σQ, as well as computer simulations of σC and σQ for simple targets.
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.
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.