Directional Splitting Research Articles

Time reversal and vector phase conjugation

The time-reversal of a monochromatic, electromagnetic-wave field is accomplished by applying a conjugate-unitary operatort to the positive time-frequency boundary fields. This produces, in general, a «directional splitting» corresponding to the evanescent and homogeneous components of the wave field. If we denote byf0 andf b those components of a boundary field ƒ which generate these respective components, then this splitting is best expressed by the relation (D z f) t =D z * ft0+B z * f tb , where «t» is the time-reversal operator,Dz is the diffraction operator (D z * the adjoint) andBz the unitary operator which propagates the homogenous wave field. This generalizes a previous relation which we used to explain the pseudoscopic real image of holography. We apply these results to our previously obtained general solution to diffraction by a perfectly conducting plane screen of arbitrary configuration. We prove that, when such a screen is placed between a radiation source and an ideal-phase conjugate mirror, the screen can become «invisible». That is, the radiation reflected back from the phase-conjugate mirror is the same whether or not the screen is present. We prove that this result holds for any ideal, reversible, additive scatterer. This invisibility is sometimes referred to as «distortion correction».