TY - JOUR
T1 - Paraxial optical fields whose intensity pattern skeletons are stable caustics
AU - Espíndola-Ramos, Ernesto
AU - Silva-Ortigoza, Gilberto
AU - Sosa-Sánchez, Citlalli Teresa
AU - Julián-Macías, Israel
AU - de Jesús Cabrera-Rosas, Omar
AU - Ortega-Vidals, Paula
AU - González-Juárez, Adriana
AU - Silva-Ortigoza, Ramón
AU - Velázquez-Quesada, Mercedes Paulina
AU - Torres del Castillo, G. F.
N1 - Publisher Copyright:
© 2019 Optical Society of America
PY - 2019
Y1 - 2019
N2 - We construct exact solutions to the paraxial wave equation in free space characterized by stable caustics. First, we show that any solution of the paraxial wave equation can be written as the superposition of plane waves determined by both the Hamilton–Jacobi and Laplace equations in free space. Then using the five elementary stable catastrophes, we construct solutions of the Hamilton–Jacobi and Laplace equations, and the corresponding exact solutions of the paraxial wave equation. Therefore, the evolution of the intensity patterns is governed by the paraxial wave equation and that of the corresponding caustic by the Hamilton–Jacobi equation.
AB - We construct exact solutions to the paraxial wave equation in free space characterized by stable caustics. First, we show that any solution of the paraxial wave equation can be written as the superposition of plane waves determined by both the Hamilton–Jacobi and Laplace equations in free space. Then using the five elementary stable catastrophes, we construct solutions of the Hamilton–Jacobi and Laplace equations, and the corresponding exact solutions of the paraxial wave equation. Therefore, the evolution of the intensity patterns is governed by the paraxial wave equation and that of the corresponding caustic by the Hamilton–Jacobi equation.
UR - http://www.scopus.com/inward/record.url?scp=85074792070&partnerID=8YFLogxK
U2 - 10.1364/JOSAA.36.001820
DO - 10.1364/JOSAA.36.001820
M3 - Artículo
C2 - 31873686
SN - 1084-7529
VL - 36
SP - 1820
EP - 1828
JO - Journal of the Optical Society of America A: Optics and Image Science, and Vision
JF - Journal of the Optical Society of America A: Optics and Image Science, and Vision
IS - 11
ER -