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Optics Express

Photosoliton modes induced by cross–phase modulation in optical media conveying bright-dark vector solitons

E. Aban Chenui, Alain M. Dikandé

Published Mar 14, 2022• 11 citations

Abstract

It is well known that high-intensity optical fields with soliton features, both bright and dark solitons, can trap and reshape photon fields of lower intensities into optical solitons by means of cross-phase modulation in optical materials with Kerr nonlinearity. In general the induced photon fields are not arbitrarily given, they are well-defined quantum states |ℓ, m〉 of a discrete spectrum which we refer to as quantum photosoliton modes. In this study we propose a scheme for the generation of quantum photosoliton states, by considering linear photon field propagating coupled to a vector high-intensity optical field with coexisting mutually transparent bright and dark solitons. It is found that features of the probe spectrum, specifically the nature, number and degeneracy of the associate quantum modes, depend on the strengths of couplings of the linear photon field to the bright and dark soliton components of the vector-soliton pump. The competition created by these simultaneous couplings leads to a rich variety of photosoliton modes, including modes that are replica of the soliton pump or translation modes of the two components of the vector-soliton pump. For the context where the optical pump consists of a single bright and a single dark soliton structures, it is found that photosoliton modes are all multiple degenerate in addition to being replica of some other modes. However, when the optical pump is a periodic multiplex of bright-dark solitons, photosoliton quantum states retain their identities (i.e. become non degenerate) but some of them are still either replica or translation modes of components of the optical pump.

DOI: 10.1364/oe.447413

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It is well known that high-intensity optical fields with soliton features, both bright and dark solitons, can trap and reshape photon fields of lower intensities into optical solitons by means of cross-phase modulation in optical materials with Kerr nonlinearity. In general the induced photon fields are not arbitrarily given, they are well-defined quantum states |ℓ, m〉 of a discrete spectrum which we refer to as quantum photosoliton modes. In this study we propose a scheme for the generation of quantum photosoliton states, by considering linear photon field propagating coupled to a vector high-intensity optical field with coexisting mutually transparent bright and dark solitons. It is found that features of the probe spectrum, specifically the nature, number and degeneracy of the associate quantum modes, depend on the strengths of couplings of the linear photon field to the bright and dark soliton components of the vector-soliton pump. The competition created by these simultaneous couplings leads to a rich variety of photosoliton modes, including modes that are replica of the soliton pump or translation modes of the two components of the vector-soliton pump. For the context where the optical pump consists of a single bright and a single dark soliton structures, it is found that photosoliton modes are all multiple degenerate in addition to being replica of some other modes. However, when the optical pump is a periodic multiplex of bright-dark solitons, photosoliton quantum states retain their identities (i.e. become non degenerate) but some of them are still either replica or translation modes of components of the optical pump.

Abstract The generation of high‐intensity optical fields from harmonic‐wave photons, interacting with dark solitons via a cross‐phase modulation coupling, both propagating in a Kerr nonlinear medium, is examined. The focus is on a pump consisting of time‐entangled dark‐soliton patterns, forming a periodic waveguide along the path of the harmonic‐wave probe. It is shown that an increase of the strength of cross‐phase modulation coupling respective to the self‐phase modulation coupling, favors soliton‐mode proliferation in the bound‐state spectrum of the trapped harmonic‐wave probe. The induced soliton modes, which display structures of periodic soliton lattices, are not just rich in numbers, they also form a great diversity of population of soliton crystals with a high degree of degeneracy.

Photonic crystals doped with resonant atoms allow for uniquely advantageous nonlinear modes of optical propagation. The first type of mode is self-induced transparency (SIT) solitons and multidimensional localized “bullets” propagating at photonic-bandgap frequencies. Such modes can exist even at ultraweak intensities (few photons) and therefore differ substantially either from solitons in Kerr-nonlinear photonic crystals or from SIT solitons in uniform media. The second type of mode is cross coupling between pulses exhibiting electromagnetically induced transparency and SIT gap solitons. We show that extremely strong correlations (giant cross-phase modulation) can be formed between the two pulses. These features may find applications in high-fidelity classical and quantum optical communications.

Abstract We propose a nonlinear quantum walk model inspired in a photonic implementation in which the polarization state of the light field plays the role of the coin-qubit. In particular, we take profit of the nonlinear polarization rotation occurring in optical media with Kerr nonlinearity, which allows to implement a nonlinear coin operator, one that depends on the state of the coin-qubit. We consider the space-time continuum limit of the evolution equation, which takes the form of a nonlinear Dirac equation. The analysis of this continuum limit allows us to gain some insight into the existence of different solitonic structures, such as bright and dark solitons. We illustrate several properties of these solitons with numerical calculations, including the effect on them of an additional phase simulating an external electric field.

We show the formation of tunneling-induced ultraslow bright and dark solitons in an asymmetric double-quantum-well structure based on the tunneling induced transparency. In this semiconductor structure, the pump field is replaced by the electron-tunneling coupling, which can be modulated by a static electric field. With appropriate conditions, we demonstrate by modulating the intensity of the static electric field that the interplay between the group velocity dispersion and the self-Kerr nonlinearity results in the generation of dark and bright solitons with ultraslow group velocity.

We show that dark solitons in one-dimensional Bose liquids may be created by absorption of a single quanta of an external ac field, in a close analogy with the Einstein's photoelectric effect. Similarly to the von Lenard's experiment with photoexcited electrons, the external field's photon energy $\ensuremath{\hbar}\ensuremath{\omega}$ should exceed a certain threshold. In our case the latter is given by the soliton energy ${\ensuremath{\epsilon}}_{s}(\ensuremath{\hbar}q)$ with the momentum $\ensuremath{\hbar}q$, where

q

is photon's wave number. We find the probability of soliton creation to have a power-law dependence on the frequency detuning $\ensuremath{\omega}\ensuremath{-}{\ensuremath{\epsilon}}_{s}∕\ensuremath{\hbar}$. This dependence is a signature of the quantum nature of the absorption process and the orthogonality catastrophe phenomenon associated with it.