The importance of semiconductors for photonics can hardly be overestimated. Many cutting-edge optoelectronic solutions are built around the enormous potential of these media, which relies on interesting optical properties [1,2] and advanced manufacturing technologies [[3], [4], [5]] of semiconductors. An important and measurable result of research on semiconductors are studies aimed at efficient processing of optical signals through the integration of multiple components on a single chip. One of the material platforms considered for the integration are GaAs/AlGaAs structures [6,7]. Characterised by a multitude of optical nonlinear phenomena, GaAs/AlGaAs structures are highly promising, widely-studied, and still under a rapid development. A closer look into the advantages of GaAs/AlGaAs structures in the context of nonlinear integrated photonics will facilitate appropriate positioning of the study results presented herein.

The first studies of nonlinearity in structures fabricated on the basis of GaAs/AlGaAs were published in the 1970s [8,9]. They described the generation of the second harmonic in waveguides whose guiding layer was made of GaAs. Since then, interest in nonlinearity in GaAs/AlGaAs structures gained momentum and reached a peak in the 1990s. During this period, a number of solutions were presented which contributed greatly to the concept of integrated nonlinear photonics based on GaAs/AlGaAs structures. They included all-optical switching in the asymmetric Mach-Zehnder interferometer [10], a directional coupler [11], and an X-junction [12], optical muliplexing [13] and demultiplexing [14], propagation of spatial solitons [15], and nonlinear phenomena occurring during light propagation in the waveguide Bragg grating [16]. In parallel, in the mid-1990s, the concept of integrated silicon-based optoelectronic circuit was launched [17,18]. Extensive exploration of silicon photonics, observed since the early 2000s [19], has encountered some obstacles, such as, e.g., strong two-photon absorption [20] occurring in the application-relevant telecommunication wavelength band. Structures based on aluminium gallium arsenide, which operate at energies below half band gap, do not have that disadvantage [21].

Another wave of vivid interest in nonlinear integrated photonics has been observed since 2016. Many of the proposed solutions are based on waveguides made of GaAs and AlGaAs on insulator [(Al)GaAs-OI] [7,22]. Owing to a high refractive index contrast, sub-micrometre guiding structures fabricated by this technique have an ultra-high level of effective nonlinearity [22]. This has unlocked an array of possibilities in obtaining efficient nonlinear processes and demonstrating their applications. The ever-expanding collection of papers in this area include studies demonstrating the generation of supercontinuum [[23], [24], [25]], the Kerr frequency comb [22,26,27], ultrabright entangled-photon pairs [28], and other work in the field of optical signal processing [[29], [30], [31], [32]].

One of the remarkable features characterising GaAs/AlGaAs structures is a set of nonlinear mechanisms. When the photon energy is significantly smaller than the forbidden gap width, the optical field can interact with electrons without transferring them to the conduction band. At sufficient light intensity, this non-resonant, nonlinear interaction results in an ultrafast Kerr effect [33]. Another interesting and equally promising nonlinear mechanism in semiconductors is the photorefractive effect [34]. Unlike the Kerr phenomenon described above, the photorefractive effect is based on optical excitation of charge carriers. It is inhomogeneity of light distribution rather than high light intensity that is of key importance here. Under the influence of an electric field and/or diffusion, excited carriers are transferred to dark regions, where they recombine. In this way, a spatial charge distribution dependent on the light intensity distribution is generated, which becomes the source of an internal electric field. Since photorefractive materials are characterised by the electro-optical effect, the space charge field induces variations of the refractive index. Research into this type of nonlinearity has proved to be very prolific, resulting in many interesting theoretical discoveries and experimental observations [[34], [35], [36], [37]]. Studies aimed at creating reconfigurable optical circuits by using waveguiding channels induced by photorefractive solitons appear to be of particular importance [[38], [39], [40], [41], [42], [43]]. One of the essential features of photorefractive soliton waveguides is the fact that they are induced at ultra-low optical powers of microwatt values. However, since the photorefractive mechanism is based on the charge carrier transport, the formation of variations of the refractive index requires a relatively long time. The fastest photorefractive media in terms of carrier mobility are semiconductor materials. Among them, semi-insulating structures fabricated based on the GaAs/AlGaAs material system are of special importance.

As mentioned before, there has been continued and recently rising interest in semiconductor structures for applications in nonlinear integrated photonics. Therefore, attempts aimed at extending the capabilities and functionalities of semiconductor platforms with solutions using semi-insulating semiconductors, characterised by photorefractive nonlinearity, seem justified. Well-developed techniques for epitaxial fabrication of semiconductor heterostructures [5,44] and methods of controlling dopants and traps, necessary for fabricating compensated semiconductors [44], further support these attempts. A lot of research attention has been given to both bulk media and media of limited dimensionality, such as multiple quantum-well (MQW) structures [45,46]. This has resulted in expanded functionality and range of applications of GaAs/AlGaAs heterostructures, relying on standard electro-optical phenomena [47] as well as phenomena related to quantum confined excitons [45,46].

Since the axis of this article is the issue of dark soliton propagation, it is worth noting that scientific interest in the topic of dark solitary waves covers a wide spectrum of research. This type of nonlinear waves has been studied in semiconductor materials containing quantum wells but outside the photorefractive context [[48], [49], [50]]. Among the works devoted to dark solitons in other photorefractive materials, recent research of particular interest in the context of optically induced circuits includes: dark solitons excited in optical arrays [51,52], self-deflection of multiple dark solitons [53], dark solitons sequence [54] and dark surface solitons [55].The focus of this work is on soliton phenomena in semi-insulating light guiding structures made of bulk GaAs or based on GaAs/AlGaAs multiple quantum wells. Previous studies have shown that light propagation in these media is a complex nonlinear problem. Compared with other photorefractive media, GaAs/AlGaAs structures are distinguished primarily by bipolar carrier transport and negative differential resistance resulting from nonlinear electron transport [45,56,57]. Results of studies focused on the analysis of nonlinear light propagation in GaAs/AlGaAs media show that, depending on the concentration of dopants or traps and the external electric field strength, certain effects can be induced which do not occur in materials with less complex properties (hereinafter referred to as “standard media”). These include, inter alia, strong curvature of trajectories of bright soliton waves which is not caused by diffusion [58], generation of local, light-triggered oscillations of charge carrier domains [59], and their effect on soliton propagation [60]. The scope of research into dark soliton wave propagation is smaller, and results are limited to soliton solutions within a range of parameters providing a standard photorefractive response, obtained assuming the applicability of standard analytical approximations [61,62]. In this paper, we present an analysis of dark soliton wave propagation within a range of parameters extending beyond the results presented previously. The underlying motivation and the key results of the study can be summarised as follows.a)

Firstly, the analysis of standard media shows that dark solitons do not require as strong nonlinearity as that required by bright solitons. Therefore, the study has been carried out for an external electric field of intensities much smaller than those applied in the case of bright solitons;

b)Secondly, the analysis was carried out for a wide range of parameters, by which we showed that:-

propagation of dark, nondiffracting beams in structures based on GaAs/AlaAs material set is possible not only in the range of parameters in which standard approximations can be used but also outside this range,

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outside the range of applicability of analytical approximations, the photorefractive response of the studied structures can be of two types: it can exhibit strong asymmetric nonlocality of refractive index changes or it can be related to instability of charge carrier and electric field domains,

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in the case of nonlocal response, dark beams do not curve (as is the case of bright solitary waves) instead, an evolution of the beam is observed, resulting in a new, nondiffractive and asymmetric distribution of light,

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the process of stationary state formation is more complicated than predicted in previous works, both within and outside the parameter range for which standard approximations apply.

c)

Thirdly, the feasibility of extending the research to include the application-relevant, telecommunication wavelength band has been highlighted.