Abstract

The k function arises in obtaining the general solution of the eikonal equation for a homogeneous, isotropic medium and describes the shape and the structure of individual wave fronts in a wave-front train as well as the associated caustic surface. The effect that refraction by a spherical refracting surface has on this k function is examined. This general result is applied to the refraction of a train of spherical wave fronts arising from a finite object point and is illustrated by several special cases.

© 1995 Optical Society of America

The k function in geometrical optics and its relationship to the archetypal wave front and the caustic surface

Orestes N. Stavroudis
J. Opt. Soc. Am. A 12(5) 1010-1016 (1995)

Refracting the k-function: Stavroudis’s solution to the eikonal equation for multielement optical systems

John A. Hoffnagle and David L. Shealy
J. Opt. Soc. Am. A 28(6) 1312-1321 (2011)

The point-characteristic function, wavefronts, and caustic of a spherical wave refracted by an arbitrary smooth surface

Magdalena Marciano-Melchor, Esperanza Navarro-Morales, Edwin Román-Hernández, José Guadalupe Santiago-Santiago, Gilberto Silva-Ortigoza, Ramón Silva-Ortigoza, and Román Suárez-Xique
J. Opt. Soc. Am. A 29(6) 1035-1046 (2012)

Wavefronts, caustic, and intensity of a plane wave refracted by an arbitrary surface: the axicon and the plano spherical lenses

Paula Ortega-Vidals, Omar de Jesús Cabrera-Rosas, Ernesto Espíndola Ramos, Salvador Alejandro Juárez Reyes, Israel Julían Macías, Gilberto Silva-Ortigoza, Ramón Silva-Ortigoza, and Citlalli Teresa Sosa-Sánchez
J. Opt. Soc. Am. A 34(9) 1670-1678 (2017)

Maxwell equations and the k function

Orestes N. Stavroudis and Juan Bautista Hurtado-Ramos
J. Opt. Soc. Am. A 17(8) 1469-1474 (2000)