Huygen’s principle

Figure 4.14 Propagation of a plane wave between two planes Huygen s principle.

Of interest is the light intensity measured on plane II, located a distance / from plane I. Huygen s principle simply states that the field at plane II is the sum of spherical waves emanating from all points in plane I. However, the field at point A will be primarily influenced by the spherical wave at point A, with a similar relationship between the fields at points B and B. Fresnel s extension of Huygen s principle quantifies this statement. The spherical wave emanating from a differential area, dS, located at point A is... 

I. In this case, the total field at plane II must be E = e E,. Applying Huygen s principle, the field at plane II is also the integration of all the contributions from differential areas located in plane I. In other words,... 

This means that, just as mentioned above about Huygen s principle, every point where the wave function is non-zero at time t = 0 serves as a source for the wave function at a later time. Eq.(3.2) thus describes the propagation of the wave in free space between two different points and times, thereby giving the Green s function its second name the propagator. But what happens if we introduce a perturbing potential We assume that the potential is a point-scatterer (that is, it has no extension) and that it is constant with respect to time, and denote it by 1, which is a measure of its strength. If we now also assumes that we only have one scatterer, located at iq, the time development of the wave becomes ... 

An exhaustive treatment of electromagnetic wave propagation in isotropic, chiral media has been given by Lakhtakia et al. [136]. This analysis deals with the conservation of energy and momentum, properties of the infinite-medium Green s function and the mathematical expression of Huygens s principle. 

A. Lakhtakia, V.V. Varadan, V.K. Varadan, Field equations, Huygens s principle, integral equations, and theorems for radiation and scattering of electromagnetic waves in isotropic chiral media. J. Opt. Soc. Am. A 5, 175 (1988)... 

As one can see from relation (13.112), the wavefield at the point r D may be viewed at the moment of time t as the sum of elementary fields of point and dipole sources distributed over the surface S with densities dP r,t)/dn and P r,t) respectively. The interference of these fields beyond the domain D results in complete suppression of the total wavefield. Thus, the Kirchhoff integral formula can be treated as the mathematical formulation of the classical physical Huygens-Fresnel principle. 

P.D. Wilcox, R.S.C. Monkhouse, M.J.S. Lowe and P. Cawley, The use of Huygens principle to model the acoustic field from interdigital Lamb wave transducers, Review of Progress in Quantitative NDE, Vol 17, Plenum Press, New York, 1998 (in press). 

Figure 14. (a) Schematic of Huygens Principle showing construction of a new wave front 2 from the preceeding wave front S 0>) plane wave front incident on a slit of width b (c) diffraction for case where b < (d)... 

Consider a plane wave whose direction of propagation is perpendicular to a wall containing two small holes (Fig, 3,4). According to Huygens principle, these holes subsequently become sources of spherical waves which then interfere. At a distance which is large with respect to A and to d, the spherical wave in the direction of observation s can be treated as a plane wave (Fraunhofer s approximation). The path difference A between the two waves and 2 the direction s is the projection of d onto s ... 

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