Babinet's principle
In
A quantum version of Babinet's principle has been derived in the context of quantum networks.[2]
Explanation
Assume B is the original diffracting body, and B' is its complement, i.e., a body that is transparent. The sum of the radiation patterns caused by B and B' must be the same as the radiation pattern of the unobstructed beam. In places where the undisturbed beam would not have reached, this means that the radiation patterns caused by B and B' must be opposite in phase, but equal in amplitude.
Diffraction patterns from apertures or bodies of known size and shape are compared with the pattern from the object to be measured. For instance, the size of
The principle is most often used in optics but it is also true for other forms of electromagnetic radiation and is, in fact, a general theorem[citation needed] of diffraction in wave mechanics. Babinet's principle finds most use in its ability to detect equivalence in size and shape.[clarification needed]
Demonstration experiment
The effect can be simply observed by using a
Babinet's principle in radiofrequency structures
Babinet's principle can be used in antenna engineering to find complementary
where Zmetal and Zslot are input impedances of the metal and slot radiating pieces, and is the intrinsic impedance of the media in which the structure is immersed. In addition, Zslot is not only the impedance of the slot, but can be viewed as the complementary structure impedance (a dipole or loop in many cases). In addition, Zmetal is often referred to as Zscreen where the screen comes from the optical definition. The thin sheet or screen does not have to be metal, but rather any material that supports a (current density vector) leading to a magnetic potential . One issue with this equation, is that the screen must be relatively thin to the given wavelength (or range thereof). If it is not, modes can begin to form or fringing fields may no longer be negligible.
For a more general definition of Eta or intrinsic impedance, . Note that Babinet's principle does not account for polarization. In 1946, H.G. Booker published Slot Aerials and Their Relation to Complementary Wire Aerials to extend Babinet's principle to account for polarization (otherwise known as Booker's Extension). This information is drawn from, as stated above, Balanis's third edition Antenna Theory textbook.
See also
References
- ^ M. Born and E. Wolf, Principles of Optics, 1999, Cambridge University Press, Cambridge.
- ^ State transfer in highly connected networks and a quantum Babinet principle, D. I. Tsomokos, M. B. Plenio, I. de Vega, and S. F. Huelga, Phys. Rev. A 78, 062310 (2008)
External links
Light Diffraction and Babinet Principle PhysicsOpenLab