Abstract
In this paper an all-optical soliton method for calculating the Fast Fourier Transform (FFT) algorithm is presented. The method comes as an extension of the calculation methods (soliton gates) as they become possible in the cubic non-linear Schrödinger equation (3NLSE) domain, and provides a further proof of the computational abilities of the scheme. The method involves collisions entirely between first order solitons in optical fibers whose propagation evolution is described by the 3NLSE. The main building block of the arrangement is the half-adder processor. Expanding around the half-adder processor, the “butterfly” calculation process is demonstrated using first order solitons, leading eventually to the realisation of an equivalent to a full Radix-2 FFT calculation algorithm.
Highlights
Computational systems based on soliton collisions for transferring and processing data continues to be a topic which stands at the forefront of scientific research (Jakubowski et al 1996, 1997, 2001; Bakaoukas and Edwards 2009b; Steiglitz 2000).Within this framework, an earlier version of this paper originally appeared in Bakaoukas (2016)
The current paper has augmented this original work by including an extensive discussion of the optical solitons background theory as presented in the remainder of this section, a full explanation of all the basic concepts and parameters involved in the formulation of the computational system proposed for the 3NLSE-domain (Sect. 2), and a detailed analysis of all the numerical methods currently available for the simulation of optical solitons propagation down an optical fibre when the propagation parameters applicable to the system are those of the 3NLSE-domain
The material presented in Bakaoukas and Edwards (2009b), in particular, shows that in situations where optical solitons are formed within optical fibres, with appropriate practical arrangements, computationally universal systems based on collisions between first order solitons are possible using logical gates based on the ‘‘controlled’’ type of gates originally proposed by Toffoli (1980), Fredkin and Toffoli (1981)
Summary
Computational systems based on soliton collisions for transferring and processing data continues to be a topic which stands at the forefront of scientific research (Jakubowski et al 1996, 1997, 2001; Bakaoukas and Edwards 2009b; Steiglitz 2000). There is a number of studies in which the use of solitonic optical pulses for the purposes of carrying out computations has been investigated (Jakubowski et al 1996, 2001; Bakaoukas and Edwards 2009a; Blair 1998) In this present paper only temporal solitons (involving a balance between Kerr type non-linearities and dispersive effects in glass fibres) are concerned. The material presented in Bakaoukas and Edwards (2009b), in particular, shows that in situations where optical solitons are formed within optical fibres (simulations have been carried out using all the above mentioned numerical techniques), with appropriate practical arrangements, computationally universal systems based on collisions between first order solitons are possible using logical gates based on the ‘‘controlled’’ type of gates originally proposed by Toffoli (1980), Fredkin and Toffoli (1981). The CN and CCN soliton gates continue to be the essential ingredient of the computational model
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