1. Introduction

Nematic liquid crystals are soft materials possessing several nonlinear optical responses whose combination/competition can be employed to gain control of the propagation of light beams [1–4]. The NLC consist of highly anisotropic molecules with long-range orientational order, with the molecules tending to align along a common direction called the director while still exhibiting fluid-like behavior. This anisotropic nature of NLC gives rise to several intriguing optical properties, such as birefringence and high sensitivity to external stimuli, like electric and magnetic fields, temperature, and light. One of the most intriguing optical phenomena observed in NLC is the propagation of reorientational solitons (also known as nematicons) that are formed due to the balance between the light-induced torque (nonlinear response) and the restoring (elastic) molecular forces [5]. The NLC can be considered as an intensity-dependent medium where the cubic nonlinear polarisation, related to the third-order susceptibility χ⁽³⁾, gives rise to the refractive index proportional to the local optical field intensity. As a result, light wave-inducing electric dipoles in the elongated molecules leads to molecular reorientation, self-focusing phenomena, and finally to self-confinement with the formation of optically bright spatial solitons, i.e., diffraction-free light beams and waveguides [6–10]. As an intense bell-shaped light beam with finite size traverses the NLC, the light’s electric field with extraordinary polarization cause the molecules to reorient, thereby altering the local refractive index [1,7,9,11]. This refractive index change can subsequently impact the light beam’s propagation, forming bright spatial solitons in nematic liquid crystals or self-trapped light beams [7,8,10,11]. Spatial solitons in reorientable NLC, characterized by a highly nonlocal nonlinear response, have been shown to be remarkably robust in two transverse dimensions, surviving collisions and several types of perturbations, can be exceeded at milliwatt optical power levels, and also provide guidance and routing of weak optical probe signals [6,7,9,12]. Owing to the elastic forces between the molecules, the perturbation of the refractive index exceeds the beam dimensions, as the NLC exhibit pronounced nonlocality. Consequently, two-dimensional reorientational solitons are stabilized, preventing the catastrophic collapse characteristic for Kerr nonlinear materials [13,14]. The substantial reorientational response and enhanced nonlocality of NLCs promote the formation of (2D + 1)-dimensional solitons using continuous-wave (CW) beams with bell-shaped profiles at milliwatt power levels and micrometer-scale waists [15,16] even under conditions of spatial incoherence [17–19]. Owing to the strong NLC response to external fields, reorientational solitons are responsive to the control of the direction of propagation by the electric, magnetic, and optical fields [15,20–22] as well as a result of the utilization of a complex molecular arrangement in an NLC medium [23–25].

The high coupling between the light and the molecular dipoles allows reorientation even at power levels in the single milliwatt range and stable propagation of a spatial soliton at distances of a few millimeters. Even at these power levels, the significant light absorption by the NLC medium causes modulation of intermolecular forces and birefringence with temperature changes, resulting in changes in both linear and nonlinear optical properties [1,4]. In addition, as the light intensity decreases along the propagation distance, the diffraction phenomenon begins to dominate over self-focusing.

Typically nonlinear thermo-optic response exhibits a sign contrary to a reorientational one, meaning it defocuses extraordinary waves and focuses an ordinary ones. Since it is also nonlocal in nature [26–29], this response can be utilized in multiple applications. Variations in ambient temperature can modulate both the linear and nonlinear optical characteristics of NLCs [30], while localized heating induced by light absorption can lead to self-focusing or defocusing [10]. Notably, a thermo-optical effect can lead to the formation of bright thermal solitons, which preserve their profile during propagation [2,3,31], and dark spatial solitons [32], which rely on a beam self-defocusing and consist of a zero-intensity dip in a uniformly bright background, typically with a π-phase jump across the transverse profile. Dark solitons have been theoretically analyzed and experimentally studied in saturable and nonlocal NLC media [33–35]. In our previous works related to nematicons propagation, we investigated the role of competing nonlinear responses in the formation and propagation of bright spatial solitons in the case where thermal nonlinearity has a negative sign [2,10]. In such a situation, the opto-thermal effect leads, among other things, to a weakening of the reorientation self-focusing of a beam and can significantly change the propagation direction of a nematicon as a result of a significant decrease in the walk-off of the beam due to the decreased birefringence value at higher temperatures.

To better understand the interplay between reorientational solitons and bright thermal solitons, it is crucial to exploit their unique optical properties in order to optimize performance and develop novel applications. These two main nonlinear contributions, reorientational and thermal, can simultaneously be used in competing configurations to generate and control spatial optical solitons in NLC [31,36,37]. The coexistence of both soliton types can give rise to complex interactions that may diminish the overall efficiency of the NLC device. For instance, thermal soliton formation can impede the propagation of reorientational solitons, resulting in a reduced nonlinear response [2]. On the other hand, as shown in our work, both soliton types can yield a more robust and versatile nonlinear response and be used in synergistic configurations. For example, by finely controlling the intensity and polarization of the incident light and the temperature of NLC, optimizing the interplay between reorientational and thermal solitons may be possible to achieve enhanced nonlinear effects. This could improve the self-trapping of optical probe signals, optical switching, or co-propagated light beam phase modulation. The competition and enhancement of nonlinear responses in NLCs due to the presence of reorientational and thermal solitons play a vital role in determining the overall performance and potential applications of NLC-based devices. A profound understanding of the interactions between these two soliton types and the capability to control their effects can facilitate the development of more efficient and versatile NLC devices with advanced functionalities.

In this paper, we address the interaction and competition of the two primary NLC nonlinearities in response to a continuous wave (CW) input: the reorientational and the thermo-optical effects in the nematic phase. We analyze a standard planar cell significantly longer than the input beam’s diffraction length to assess the combined impact of linear diffraction and nonlinear phenomena [14,26,28,38,39]. Both nonlinearities result in pointwise alterations in the refractive index while exhibiting a highly nonlocal nature [14,40], meaning that a light-induced disturbance is much broader than the stimulating beam. Since reorientation generally prevails over thermo-optical effects in pure NLCs, we introduce a specific guest dopant to the host LC mixture to increase light absorption within a particular wavelength range [10,36]. By using one wavelength inside and another outside the absorption band of the dye, we can investigate the interplay between the two responses when excited simultaneously. As already mentioned, NLCs are uniaxial materials encompassing elongated molecules with the principal axes oriented on average along the molecular director (optic axis) n. The ordinary refractive index corresponds to eigenwaves with an electric field perpendicular to the n. The extraordinary refractive index depends on the angle θ between the optical wave-vector and n. The value and spatial distribution of θ in an NLC defines the phase velocity and diffraction of a propagating light beam. The ordinary electric field (o-wave) is always perpendicular to the director n, and its phase velocity is $c/{n_o} = c/{n_\mathrm{\ \bot }}$. In contrast, the extraordinary electric field (e-wave) lies in the same plane as the wave vector k and the director n, with a phase velocity of $c/{n_e} = c/{n_e}(\theta )$ that depends on the orientation angle θ between k and n (${n_e}(0) = {n_\mathrm{ \bot }}$):

The extraordinary wave propagates in the plane (k, n) with a Poyting vector tilted with respect to the wave vector by the walk-off angle [7]:

2. Temperature effects on extraordinary refractive index n_e(θ) and the sign of nonlinearity

The refractive indices of NLCs are temperature-dependent, with n_e typically decreasing as the temperature increases and n_o either increasing or decreasing depending on the material’s properties [41–43]. The exact relationship between temperature and refractive index depends on the specific NLC material in which it remains in the nematic phase. The nonlinear optical properties of NLCs, such as the nonlinear refractive index and the third-order susceptibility, are also influenced by temperature [42]. In some instances, the sign of the overall nonlinearity (positive or negative) can change as the temperature varies. This change in the sign of nonlinearity can significantly impact the behavior of NLC-based devices, such as the formation and propagation of solitons, optical switching, and light modulation.

The mechanisms responsible for temperature-induced changes in the sign of nonlinearity depend on several factors, including the interplay between thermal and reorientational nonlinearities, the temperature dependence of the refractive indices, and the molecular structure of the NLC material. Furthermore, temperature variations result in modulations of the intermolecular links, thereby altering the overall response and modifying both the birefringence and the nonlinearity of the material [1].

In an NLC slab with a uniform director distribution, corresponding to the angle $\mathrm{\theta}_o$, concerning the z-axis (Fig. 1(a)), the propagation of an extraordinary beam is related to the walk-off δ, which quantifies the angular displacement between the wave and Poynting vectors (given by 1.2), and by an equivalent reorientational nonlinearity n_2R related to the degree of beam confinement [9,15,40]:

 

Fig. 1. (a) NLC sample geometry; (b) ordinary (θ = 0°) and extraordinary (θ = 90°) refractive indices for the 6CHBT NLC for λ = 1064 nm (magenta and black line) and λ = 532 nm (red and blue line); (c) comparison between the extraordinary refractive index n_e (θ = 15°) (black line with black squares) and nonlinear coefficient n_2R (θ = 15°) for λ = 1064 nm (red line with red circles) plotted as a function of temperature.

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In general, reorientational and thermo-optic effects are usually decoupled and thus can be employed to generate [7,9] and control nematicons [5,10,15,31].

For the thermal nonlinearity ${n_{2T}} \sim \sigma \frac{{dn}}{{dT}}$, with σ being the absorption coefficient and n being the ordinary or extraordinary refractive index. For ordinary waves, n_2T is usually positive, leading to a self-focusing nonlinear response. For extraordinary waves, the sign of n_2T depends on the initial orientation angle θ₀, and can change the sign while changing the angle θ. As anticipated, n_2T is proportional to the absorption coefficient and thus can be enhanced by using suitable dopants. In this way, using the dye in the right concentration can lead to overall nonlinearity being positive or negative.

The experimental investigation was carried out in a planar nematic liquid crystal cell composed of two glass substrates with a gap between them of d = 80 µm. Both substrates were spin-coated using a ZLI-2650 polyimide (Merck). Before gluing the NLC sample, each substrate was mechanically treated by the rubbing technique to ensure the homogeneous alignment of the long axis of the molecules at θ₀ = 15° with respect to the z-axis, as schematically sketched in Fig. 1(a). We used two Gaussian beams of different wavelengths and polarizations to decouple and investigate the contributions of distinct nonlinear responses. Both beams were coupled into the NLC cell after being focused with a microscope objective to a waist of about 5 µm. The width of both beams before the microscope objective was chosen to provide more or less the same waist after focusing. The two wave beams were launched collinearly by adjusting their input wave vector tilt to make the Poynting vectors overlap (Fig. 1(a)). The beam evolution in the yz-plane was recorded by collecting the out-of-plane scattered light with a CCD camera and a microscope. The beam profile in the xy-plane was recorded by collecting the transmitted light through the cell after a propagation distance of 1.5 mm. To investigate independently the particular beam evolution when co-propagate with a beam characterized by different wavelengths, a bandpass filter was utilized to visualize only one wavelength of interest. For two Gaussian beams, we employed an Nd:YAG laser emitting at 1064 nm as an intense IR beam outside the absorption band and a frequency-doubled Nd:YAG laser operating at 532 nm as a co-propagating green beam inside the absorption band.

The cell was filled with 6CHBT nematic liquid crystal [-4-(trans-4'-hexylcyclohexyl)isothiocyanatobenzene] [44] (λ = 1064nm: n_o = 1.49, n_e = 1.63 and λ = 532nm: n_o = 1.52, n_e = 1.68 at T = 20°C), doped with 0.05% of Sudan Blue II dye, with an absorption peak localized at λ = 604 nm and significantly enhanced absorption for λ = 532 nm [45].

Figure 1(b) illustrates the dependence of ordinary and extraordinary refractive indices for 6CHBT at λ = 532 nm and λ = 1064 nm, respectively, as a function of temperature. In the case of the 6CHBT nematic liquid crystal used in the experiments, the extraordinary refractive index consistently decreases, while the ordinary refractive index increases with temperature. This indicates that the extraordinary refractive index ${n_e}({{\theta_0}} )$, depending on the initial orientation, decreases or increases as a function of temperature. The refractive index for an extraordinary beam with an initial molecular orientation at ${\theta _0} = 15\mathrm{^\circ }$ increases with temperature.

Figure 1(c) presents the extraordinary refractive index for ${\theta _0} = 15\mathrm{^\circ }$ as a function of temperature. For temperatures lower than 26°C, the ${n_e}(\theta )$ decreases, indicating that in this temperature range, the thermal influence, i.e., thermo-optic response, takes on a negative sign. For temperatures between 26 ÷ 32°C the ${n_e}(\theta )$ remains unchanged despite the increase in temperature, signifying that the effect of thermal nonlinearity is negligible. For temperatures above 32°C, the ${n_e}(\theta )$ increases, which means that the thermal nonlinearity in this range takes on positive values and exhibits a focusing character. Figure 1(c) also graphs the curve from the Eq. (1.3) – considering the temperature ranges characteristic for ${n_e}(\theta )$ changes. Also three regions can be distinguished: initially, starting from T = 20°C the nonlinear coefficient is approximately constant, then for temperatures between 26 ÷ 32°C it slightly increases, and finally, for temperatures above T = 32°C it decreases. This theoretical expectation demonstrates that thermo-optic modulation of NLC properties is a viable approach to reorientational and thermal solitons interaction and thus can be implemented for fully thermo-optic signal readdressing.

3. Thermal and reorientational solitons

We initially studied the two nonlinear responses individually, including a comparative analysis of the positional stability in the nonlinear regime. Figure 2 demonstrates the propagation of a visible green beam with ordinary (TM) polarization and an IR beam with extraordinary (TE) polarization, launched in the same Poynting vector directions. As depicted in Fig. 2(a-b), the natural diffractive broadening of the low-power ordinary polarized green beam was counterbalanced by the thermal self-focusing at P_GREEN = 4 mW, forming a green thermal bright soliton, which preserves its spatial profile at a distance corresponding to an NLC cell length of 1.5 mm.

 

Fig. 2. Individual propagation and nonlinear response of a visible (green beam λ = 532 nm) and infrared beam (λ = 1064 nm) with orthogonal polarization TM and TE, respectively. Acquired images of (a-b) green TM-beam evolution in yz- and xy-plane for low power P_GREEN = 0.4 mW and thermal nematicon generation for high power P_GREEN = 4.0 mW respectively; (c-d) near-infrared TE-beam for low power P_IR ∼ 0.5 mW and reorientational self-focusing at optical power P = 4.0 mW respectively. Right panels in (a-d) present the optical field in the xy-plane, at the output of the NLC cell, at z = 1.5 mm; Comparison of the stability of induced solitons: thermal and reorientational: (e-g) stability of the thermal nematicon (λ = 532 nm, TM-polarization) at the output of the cell (z = 1.5 mm). (e) Normalized beam width and (f) position along the x- and the y-axis, solid and open markers, respectively; (g) representation of the spread of the beam center position within 25 seconds period and (h-j) corresponding results for the reorietational nematicon (λ = 1064 nm, TE-polarization).

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Similarly, when employing the extraordinarily polarized IR beam, reorientational self-focusing was observed at P_IR = 4 mW, resulting in light confinement and also the propagation in the form of a bright reorientational soliton (Fig. 2(c)-(d)).

Thermal solitons arise from self-provided heating by the beam and thus by thermal fluctuations in the NLCs [28,3,1]. The presence of thermal fluctuations aids in dissipating energy and stabilizing the soliton structure. This thermal energy contribution renders the position versus time of thermal solitons more stable, as the fluctuations can continuously balance the forces acting on the soliton, maintaining its shape and position. On the other hand, due to the long-range correlated noise in soft matter, these nematicons undergo transverse trajectory time-depended fluctuation over long propagation distances [46,47]. Consequently, when comparing the position versus time for thermal and reorientational solitons, thermal solitons tend to exhibit more stable behavior. Indeed, as illustrated in Fig. 2(e-j), the change in soliton width, analyzed at the exit of the cell after a propagation distance of 1.5 mm, shows much more excellent stability over time (more minor fluctuations) for the thermal soliton compared to the reorientational soliton. If the position of the soliton is analyzed as a function of time at the output of the cell, the thermal soliton also shows higher stability.

3.1 Competing effect at room temperature:

As outlined in Fig. 1(f), at room temperature, for an IR extraordinary beam, the refractive index ${n_e}(\theta )$ decreases with temperature meaning that the thermal nonlinearity exhibits negative values (n_2T < 0). This indicates that the induced temperature change by the absorbed TM-polarized green beam results in a decrease in the extraordinary refractive index ${n_e}(\theta )$ for an IR beam with TE polarization. This, in turn, leads to a detrimental effect of the thermal nonlinearity on the reorientation nonlinearity, ultimately causing a defocusing effect for the infrared beam. Figure 3(a) presents an xy-plane view after propagation distance z = 1.5 mm (left panel) and the beam evolution in yz-plane (right panel) of the reorientational infrared soliton (P_IR = 3.5 mW) in the absence of simultaneous green beam propagation. The IR beam propagates in the form of a nematicon, as evidenced by the circular spot at the output. In Fig. 3(b), an output photo of a nematicon in the xy-plane is displayed when a low-power TM green beam (P_GREEN = 2 mW) is launched simultaneously (Fig. 3(c)). This low-power green beam does not cause significant thermal effects and therefore does not cause any noticeable change in the propagation of the IR nematicon. As the power of the green beam increases and a thermal soliton is generated (Fig. 3(e)), a defocusing effect for the infrared beam occurs (Fig. 3(d)). The IR nematicon’s width varies with propagation due to the green beam-induced defocusing effect (Fig. 3(d)), which in turn reduces the available birefringence and consequently the magnitude of the reorientational response reflected in the elongation of the period of the IR breather (Fig. 3(f)). These findings are in line with previously obtained results for IR and green beam propagation when both beams had TE polarizations [2,5,30,31]. In the analyzed case, the effect produced by the TM green beam forming a thermal soliton is analogous to that produced by the green beam with TE polarization: it reduces the effective refractive index for the beam with extraordinary polarization, thereby causing a defocusing effect.

 

Fig. 3. Competing nonlinearities in NLC with dye dopant at room temperature T = 20°C. (a-e) Acquired output images in the xy-plane (left panels) at the output of the NLC cell, at z = 1.5 mm and a top-view in the yz-plane (right panels) for TE-polarized infrared beam λ = 1064 nm, at fixed power P_IR = 3.5 mW and for increasing green TM-polarized beam. (a) Evolution for only IR beam P_GREEN = 0.0 mW; (b) evolution of IR beam propagating with the ordinary green beam with power P_GREEN = 2.0 mW; (c) view for a visible beam equals P_GREEN = 2.0 mW, corresponding to (b); (d) evolution of IR beam propagating with the ordinary green beam with power P_GREEN = 4.0 mW; (e) view for a visible beam equals P_GREEN = 4.0 mW corresponding to (d); (f) Normalized IR beam widths (w(z) / w₀) along propagation distance (P_IR = 3.5 mW), for the λ = 532 nm beam power in the range of 0.0 ÷ 4.0 mW, black to grey lines, respectively.

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3.2 Coexistence of thermal and reorientational soliton

Upon increasing the temperature of the sample to 30°C, we reach a regime where n_2T ∼ 0 for the extraordinary beam, as indicated in Fig. 1(f), implying that the effect of thermal nonlinearity on the propagation of the extraordinary beam is negligible. Figure 4(a-b) illustrates the propagation of the IR extraordinary beam in the form of a reorientational soliton with a power of P_IR = 6 mW, and the ordinary green beam in the form of a thermal soliton with a power of P_GREEN = 2.5 mW. Please note that the difference in powers, compared to previous results, is attributed to the variations in sample temperature at which these measurements were taken. Figure 4(c) investigates the impact of the ordinary green beam on the propagation of the IR soliton. The IR beam power is maintained at P_IR = 6 mW, while the power of the green beam changes from P_GREEN = 0.5 mW (diffraction, no thermal effects) to P_GREEN = 2.5 mW, at which the thermal nonlinearity significantly affects the ordinary refractive index and a soliton is observed (inset in the bottom right corner of the figure). However, the propagation of the extraordinary IR beam in the form of a nematicon remains unaffected by the induction of the thermal soliton for the ordinary green beam, as shown in the graph presenting the changes in the IR beam width as a function of the green beam power at the cell output after propagating a distance of z = 1.5 mm.

 

Fig. 4. Coexistence of two orthogonally-polarized solitons: reorientational nematicon and thermal soliton in dye-doped NLC at temperature 30°C. (a) A reorientational nematicon (top view) induced by a TE-polarized infrared beam at optical power P_IR = 6.0 mW; (b) A thermal nematicon (top view) induced by a TM-polarized beam within a visible spectral band (λ = 532 nm) at optical power P = 2.5 mW. (c) Normalized infrared beam widths at propagation distance z = 800µm, co-propagated with the λ = 532 nm beam of power within the range of 0.5 ÷ 2.5 mW. The insets present the optical field distribution at the output of the NLC cell (z = 1.5 mm) – infrared (top panels) and green light (bottom panels). (d) Normalized green beam widths at propagation distance z = 800µm, co-propagated with the λ = 1064 nm beam of power within the range of 0.5 ÷ 6.0 mW. The insets present the optical field distribution at the output of the NLC cell (z = 1.5 mm) – green light (top panels) and infrared (bottom panels). The orange dashed line in (c) and (d) represents the average value of the datapoints on the graph.

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Similarly, Fig. 4(d) displays the effect of the IR extraordinary beam on the ordinary green thermal soliton propagation. The green beam has a power of P_GREEN = 2.5 mW and propagates as a thermal soliton; the power of the infrared beam changes from P_IR = 0.5 mW (no nonlinear effects) to P_IR = 6 mW, the power at which the infrared beam propagates in the form of a nematicon. A graph presenting the changes in the width of the green thermal soliton at the output of the cell for increasing infrared beam power shows no effect of the latter on the propagation of the green beam. These results confirm that, at a temperature of 30°C, the thermal nonlinearity enabling the formation of a thermal soliton for the ordinary beam does not impact the simultaneous propagation of the extraordinary infrared beam in the form of a nematicon. Both nematicon and thermal soliton, launched exactly along the same path, propagate within the system without mutual influence.

3.3 Mutual enhancing

To exploit the final temperature range, wherein the extraordinary refractive index ${n_e}({{\theta_0}} )$ increases with temperature, the sample’s temperature was set at 40°C. As before, the two orthogonally polarized beams were launched collinearly by adjusting their input wave vector tilt to make the Poyting vector overlap. Figure 5(a-b) shows the propagation of both beams with powers insufficient to induce nonlinear effects: clearly none of them is individually able to self-confine at the given input power. When increasing the power of the green beam, a focusing effect is observed on both beams (Fig. 5(e-d)). Ultimately, as shown in Figs. 5(e-f), increasing the power of the green beam up to P = 0.7 mW and generating a thermal soliton (Fig. 5(e)) leads to the focusing of the infrared beam, meaning that the temperature rise and the nonlinearity induced by the green beam, consequently, increase the extraordinary refractive index for infrared beam, enhancing the focusing of the infrared beam and leading to nematicon creation (Fig. 5(f)). The graphs in Fig. 5(g-h) plots a beam width as a function of propagation distance for increasing green beam power, for green and infrared propagation, respectively.

 

Fig. 5. Enhancing nonlinear response by the two orthogonally-polarized solitons at temperature 40°C: (a) propagation of the single beam of a wavelength λ = 532 nm, TM-polarized, of optical power P_532nm = 0.2 mW; (b) propagation of the single infrared beam, TE-polarized, of a power P_IR = 3.0 mW. The self-focusing effect supported by a co-propagated visible beam (λ = 532 nm) of a TM-polarization and optical powers (c-d) P_532nm= 0.4 mW and (e-f) P_532nm= 0.7 mW. Pictures in (c-f) present a filtered view of a particular wavelength in the case of two beams co-propagation. The right panels in subfigures (a-f) present the optical field distribution at the output of the NLC cell (z = 1.5 mm). (g) Normalized green visible beam widths along propagation distance, simultaneous propagation with P_IR = 3.0 mW, TE-polarized, for the λ = 532 nm beam powers equal 0.2 mW, 0.4 mW, 0.5 mW, 0.6 mW and 0.7 mW, dark to light green lines, respectively; (h) Normalized IR beam widths along propagation distance, P_IR = 3.0 mW, for P_532nm equal 0.0 mW, 0.4 mW, and 0.7 mW, black to grey lines, respectively;

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In order to confirm that the enhancement of nonlinearity does not occur at the expense of changing the polarization of one of the solitons and that there are still two solitons with orthogonal polarizations in the system, Fig. 6 presents the output distribution images for both the infrared and green beams with two different polarizer settings in front of the camera.

 

Fig. 6. Enhancing nonlinear response by the two orthogonally-polarized solitons at temperature 40°C. The optical field distribution at the output of the NLC cell (z = 1.5 mm): (a) infrared (P_IR = 3.0 mW) and (b) green light (P_GREEN = 0.7 mW), filtered view. Pictures were recorded with an additional polarizer placed in front of the camera with an optical axis along TE- and TM-polarization directions, left and right panels, respectively.

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To sum up our work, we have demonstrated the relevant aspects of reorientational and thermal solitons in nematic liquid crystals. On the basis of the presented experimental results, we have shown that, depending on the optical properties of the liquid crystal medium, which are highly temperature-dependent, it is possible to achieve more precise control of the reorientation soliton by simultaneous beam co-propagation with the thermal soliton at wavelengths within an increased absorption wavelength band. As a result, by designing the appropriate initial orientation of NLC molecules, we can obtain three characteristic temperature ranges in which the coexistence of reorientation and thermal solitons will be associated with their competition (the reduction of the nonlinear response), independent propagation or support based on the mutual amplification of the nonlinear response of the medium. The deeper insight and better understanding of the interplay between different nonlinear mechanisms present in nematic liquid crystals provided in this work potentially increases the possibilities of exploiting NLC structures in applications such as integrated photonic devices, all-optical signal processing, or as a technique for optical switching systems. The deeper insight and better understanding of the interplay between different nonlinear mechanisms present in nematic liquid crystals provided in this work potentially increases the possibilities of utilizing NLC structures in applications such as integrated photonic devices, all-optical signal processing, or as a technique for optical switching systems, as well as contributing to a better fundamental understanding of the light-matter interaction in nematic liquid crystals.