Strong Focusing–The LOGO

          So what is the logo all about?  As an electromagnetic wave field propagates in a structured medium, the structure is first imparted to the phase of the evolving wave field. As the wave field continues to propagate, the wave intensity begins to feel the structure.  Think of a lens focusing a bundle of rays.  Very near the lens there is little intensity variation, but a convex lens can bring the rays to a focus where the intensity changes prominently.  A propagation medium with a turbulent refractive index structure can be thought of as a collection of random lenses. Shimmering images above a hot roadway and twinkling stars are examples of propagation in disturbed media, in this case the turbulent atmosphere.  The random intensity fluctuation is called scintillation.

          The scintillation phenomenon has intrigued scientists for decades.  As it came to be understood, scintillation was used to determine the characteristics of light sources and media that are not accessible to direct measurement.  Scintillation can be a nuisance for satellite radio transmission and remote earth sensing. 

          The theory of scintillation can be intimidating, but riding the wave of the computer revolution  inexpensive computers can be used to simulate the phenomenon providing insights that would be very difficult to ascertain from data analysis and theory.  Strong focusing, a scintillation phenomenon that generates intensity structures that require advanced mathematics to characterize, can be realized with a few hundred lines of straightforward computer code.

                The figure below illustrates a simulation.  The illumination is from the left.  The first image is the structure variation in the medium.  Because of the particular characteristics of this realization, the wave field propagating through the medium very quickly develops dramatic fractal-like structure.  The mathematician Michael Berry dubbed these fascinating structures diffractals.  As the field continues to propagate, however, the structure eventually evolves to a uniform speckle field.  Since free propagation is reversible, the field structure still retains the complete history of how it came to its present state.  MATLAB codes that will reproduce the structure are available with my book. 

                In remembrance of a colleague, Stanley Flatte, the copy of the cover of the July 1984 issue of Applied Optics is the first numerical simulation of this type.  Although the computation was performed on a Cray super computer, it has substantially lower resolution and dynamic range than what can be reproduced today on a high-end PC.

About Chuck

Retired research engineer. Recently published book "The Theory of Scintillation with Applications in Remote Sensing," John Wiley IEEE Press, 201
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