Page 14 - Phase Space Optics Fundamentals and Applications

Preface

t is no simple task to characterize the importance of phase-space
methods in the optical sciences. Geometrical optics, formally re-
I lated to classical mechanics, has benefitedimplicitlyandexplicitly
from phase-space concepts since Hamiltonian and Lagrangian optics
were first formulated. In comparison, phase-space optics of coherent
wavefronts, namely, the use of the Wigner distribution functions and
of the ambiguity function, constitutes a more recent development,
and the Wigner distribution remains far from being integrated into
the canon of standard tools used by the optics community.
Optical engineers and researchers are polarized on the use of phase-
space optics. Many remain intrigued, but skeptical toward a math-
ematical formalism that appears theoretically demanding, without
providing obvious complementary information for describing optical
phenomena. On the other end of the spectrum one can find a small,
but fast-growing community that is enchanted by the beauty and sim-
plicity of phase-space optics, revealing itself even with only a scant
familiarity with the theoretical framework.
To understand this devotion, it is important to recognize the unique
position that optics holds in science and engineering. Optics is both
a subject of basic research and an enabling technology. Fundamental
questions about the quantum nature of light, and its interaction with
matter, are at the core of modern physics. At the same time, there is a
rich history of optical instruments pivotal to ground-breaking discov-
eries in astronomy, biology, communications, and many other disci-
plines. In the past half century, the optical sciences have developed at
an astounding pace. Perhaps with the exception of microelectronics,
optics has become the most vibrant technology resting at the intersec-
tion of different brands of research.
As a consequence, different optical sciences have developed unique
and effective models to describe light propagation and the interac-
tion of light with matter. Notwithstanding the universal validity of
Maxwell’s equations, or quantum electrodynamics, it is often more
effective to describe light propagation based on specific models (rays,
scalar waves, or Gaussian beams) than to consider the full complex-
ity of the electrodynamic wave field. All models of light propagation

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