Open AccessWigner functions defined with Laplace transform kernels
Author(s) -
Se Baek Oh,
Jonathan C. Petruccelli,
Lei Tian,
George Barbastathis
Publication year - 2011
Publication title -
optics express
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.394
H-Index - 271
ISSN - 1094-4087
DOI - 10.1364/oe.19.021938
Subject(s) - wigner distribution function , laplace transform , two sided laplace transform , green's function for the three variable laplace equation , kernel (algebra) , inverse laplace transform , mathematical analysis , laplace transform applied to differential equations , mathematics , fourier transform , physics , pure mathematics , quantum mechanics , fractional fourier transform , fourier analysis , quantum
We propose a new Wigner-type phase-space function using Laplace transform kernels--Laplace kernel Wigner function. Whereas momentum variables are real in the traditional Wigner function, the Laplace kernel Wigner function may have complex momentum variables. Due to the property of the Laplace transform, a broader range of signals can be represented in complex phase-space. We show that the Laplace kernel Wigner function exhibits similar properties in the marginals as the traditional Wigner function. As an example, we use the Laplace kernel Wigner function to analyze evanescent waves supported by surface plasmon polariton.