Design, transform and control of optical field in discrete optical system: an example

Abstract

A discrete optical system can broaden the spatial distribution of the input light through optical coupling in array waveguides, just like diffraction in continuous media. Here, we theoretically demonstrate several kinds of control methods of optical field propagation in a discrete optical system, which is composed of an Airy fiber with two perpendicular arrayed cores. A brief transform mechanism between Gaussian and Airy beam propagation in such a fiber is presented. The wavefront of the output beam from the Airy fiber is actually dependent on the phased arrayed modulation of coupling array cores. Except the optical wavelength changing, we propose two new methods, including fiber length and bending-induced refractive-index changing, to accomplish that modulation. The calculation results show that these new methods are very effective for the Airy phase modulation. By combining these methods and controlling the corresponding parameters, the Gaussian beam, the one-dimension Airy beam, and the two-dimension Airy beam can be obtained by one same Airy fiber. These methods are also generally applicable to the other discrete optical system and can be extended to generate any other types of optical beams, such as Bessel beams and Mathieu beams.The Airy beam (AB) have propagation-invariant intensity profile and exhibit 'self-healing' features 1-3 . In particular, such a beam has an ability to remain transverse accelerating during propagation 4 , which moves on a parabolic trajectory very much like a body under the action of gravity. Owing to these unique properties, Airy beams have found many potential applications, such as optical micro-manipulation 5,6 , imaging technology 7 , surface plasmon polaritons 8, 9 and laser micromachining 10 . The direct generation of the Airy beam requires combining phase and amplitude modulation by imposing a cubic phase on a Gaussian beam and then taking its Fourier transform using a lens. Several AB generations and controls using bulk optic configuration were reported, such as spatial light modulator (SLM) 1, 11 , continuous phase mask 12 , nonlinear photonic crystal 13,14 , and optically induced refractive index gradient 15 . In our previous work 16,17 , a one/two-dimensional (1D/2D) Airy-like beam technique was reported based on array waveguides instead of a cubic phase plate. Such an Airy fiber has a small size, easy handling, stable and strong anti-jamming capability.In the discrete optical system, waveguide arrays have been used to engineer the diffraction properties of optical wave fronts 18 . In this paper, we study theoretically the propagation properties of light in a discrete optical system of the Airy fiber with a 2D arrayed-core. We focus on studying the transform mechanism between Gaussian and Airy beam propagation in such a fiber. To control the propagation dynamics of light in the fiber, several modulation methods are introduced by changing the controlling parameters. We further demonstrate the consistency and validity of these methods and reveal that the propagation proper...