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Optical display of the Airy function and transient wave propagation in a dispersive medium
The display of an Airy function via an optical image processing technique is
demonstrated. Using a two-dimensional object with a cubic amplitude transmittance, one
can observe a Fourier transformed image of which intensity variation is identical to that of
the Airy function. A lens system is used to achieve the Fourier transformation of the object
which is a two-dimensional binary filter. A set of computer simulations are performed
prior to the optical experiments.
Using the same method of optical display, the transient wave propagation in a
dispersive medium is optically displayed based on the analogous relationship found
between two equations: One is the Fourier form of a transient wave field propagating in a
dispersive medium and the other is an equation of the diffraction pattern of an object
constructed with two juxtaposed two-dimensional filters. A theoretical analysis is provided
along with computer simulations. The use of a Spatial Light Modulator is proposed as the
source of the input object in the optical experiment.