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Backscattering of electromagnetic missiles

Conventional radar pulses spread so that the energy reaching a reflecting target at range r decreases as r exp -2. The energy echoed from the target also decreases as r exp -2, so that the energy backscattered to the transmitter is proportional to the product, i.e., to r exp -4. Pulses of finite total energy that satisfy Maxwell''s equations need not decrease as r exp -2, but can instead decrease much more slowly, for instance as r exp -epsilon where epsilon is a positive number that can be chosen as small as desired. Such pulses are referred to as electromagnetic missiles. Here, the echo backscattered when an electromagnetic missile encounters a plate target is studied. By analogy with conventional radar, it might be expected that the energy of the echo would be proportional to r exp -2(epsilon). Instead, the reflected energy decreases even slower, proportional to r exp -epsilon, so that no squaring occurs, resulting in a larger than expected radar return.