Abstract
We use slow-varying amplitude approximation (SVA) for the wave equation to study both analytically and numerically propagation of an electromagnetic beam in the waveguide structure with parabolic susceptibility spatial dependence. Such a structure is similar to the harmonic oscillator in quantum mechanics. We analyze this structure as a single mode guide and introduce the notion of number of “photons” in the mode. In particular, we pay special attention to the possibility of effective build-up of the coherent and spatially squeezed vacuum states of the mode that can be of interest for a number of practical applications. The way to provide these types of mode excitation is suggested. Several applications for controlling the mode composition of an electromagnetic wave in the parabolic index-gradient waveguide for various frequency ranges are considered.
Highlights
To date, a number of hybrid optoelectronic computing devices require transmitting of electromagnetic wave “packets” along waveguide structures from a nanoscale “source” to a nanoscale “receiver” [1,2]
We demonstrate how the well-known analogy between the propagation of light beams in wave optics and the movement of micro-particles in quantum mechanics can be applied in optimization procedures for elements and systems of optoelectronic computing devices
The coherence coherence length length of of the the spatial spatial transverse transverse oscillations oscillations of of the the beam beam in in the the non-ideal non-ideal waveguide obtained through the integral of overlapping for different initial waveguide obtained through the integral of overlapping for different initialstates. Is it possible to implement into practice the generation of the coherent and spatially squeezed it possible to implement into practice the generation of on thethe coherent and spatiallyintegrated squeezed statesIsdescribed above?
Summary
A number of hybrid optoelectronic computing devices require transmitting of electromagnetic wave “packets” along waveguide structures from a nanoscale “source” to a nanoscale “receiver” [1,2]. The simplest illustrative examples are the graded-index fibers with a close to parabolic index profile This form of spatial inhomogeneity for dielectric constants leads to the fact that a Gaussian input beam Photonics 2019, 6, 84 inhomogeneity for dielectric constants leads to the fact that a Gaussian input beam (somewhat displaced against the center of the fiber core) will oscillate without fully reaching the edges of the core region This behavior, which allows us to reduce the energy dissipation and distortion of the wave packet shape, is similar to the oscillations of a coherent wave packet in a quantum harmonic center of the fiber itcore) will oscillate without fully edges of the core region. Structure, namely to build-up of a coherent or spatially squeezed state (b)
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