Abstract
We discuss a method to transform any optical field, with finite frequency bandwidth, into a shape invariant beam with transverse scaling, dependent on the propagation distance. The method consists in modulating the field with a quadratic phase of appropriate curvature radius. As a particular application, we employ the method to extend the existence region of a finite non-diffracting field to an unbounded domain.
Highlights
Propagation of a coherent or partially coherent light beam is an important process in applied and theoretical optics
Other optical fields, which we refer to as scaled propagation invariant (SPI) beams, preserve their shapes in an unbounded propagation range, at the expense of a re-scaling in their transverse extensions
By employing Eq (2), we obtain the complex amplitude of the phase modulated sinc-Gaussian (PMSG) field g(x, y) exp[i10 (x2 y2 ) / p2] g0 (x, y)
Summary
Propagation of a coherent or partially coherent light beam is an important process in applied and theoretical optics. By employing Eq (2), we obtain the complex amplitude of the phase modulated sinc-Gaussian (PMSG) field g(x, y) exp[i10 (x2 y2 ) / p2] g0 (x, y). The transverse amplitude of G0(u,v) corresponds, as expected, to an annular field of radius 0, whose transverse section is a Gaussian; and the plot in Fig. 4 (c) confirms that the Fourier spectrum G(u,v) inherits the shape of g0(x,y).
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