Kerr Nonlinearity in germanium selenide nanoflakes measured by Z-scan and spatial self-phase modulation techniques and its applications in all-optical information conversion

Yue Jia; Zhongfu Li; Muhammad Saeed; Jie Tang; Houzhi Cai; Yuanjiang Xiang

doi:10.1364/OE.27.020857

1. Introduction

In the recent decades, since graphene was discovered in 2004, different types of two-dimensional (2D) materials have been explored extensively [1,2]. In addition to further exploring the new features of the existence 2D materials, retrieval of the novel 2D materials have been extended recently to comprise the close neighbors of the V-family element, called, IV−VI binary analogous flakes like GeSe, SiTe and GeS [3–6]. These compounds possess attractive properties such as, high piezoelectric and thermoelectric performance [7], superconductivity [8], and exempli gratia carrier bipolarity [9]. Among them, Germanium-based thiocompound (GeSe) has been widely studied due to its high stability, unique photoelectric properties, richness, environmentally sustainable, low toxicity etc. GeSe is a chair conformation consisting of six-membered rings for each layer and each cation of this ring structure is tri-coordinated, leaving only one single pair of electrons pointing to the interlaminar spacing, so it is sensitive to interlaminar coupling. The GeSe nanoparticles are dynamically stable in an independent state, and possess similar semiconductor behaviors to that of phosphorene in theoretical studies [10,11]. Meanwhile, the 2D material GeSe with IV−VI p-type semiconductors have narrow indirect band gaps at 1.37 eV, which is usually constructed with a puckered layer familiar to phosphorene, however, the difference is that in the available experimental research, GeSe occurs within the layer or GeS is outside the layer [12]. GeSe nanoflake photo switching behaviors have been reported, which shows a similar light response to TMDCs [13]. The theoretical calculations show that due to the destruction of the inversion symmetry, the strong quantum confinement effect, electrical properties and valley polarization are all caused by the destruction of the inversion symmetry. The inherent physical properties and applications in functional equipment for these materials remain still lack of methodological understanding [14,15]. In particular, powder metallurgy, which is close to silicon (1.12 eV) in volume, is expected to undergo indirect direct remelting, similar to powder metallurgy [16–18]. The electronic structure of GeSe is in a heated debate; however, the existing process variable for GeSe has not been studied experimentally.

The 2D materials IV−VI binary analogous flakes with NLO process have attracted great attention because of their potential applications in various photonic and optoelectronic equipment [19–21]. The NLO responses of these 2D materials under low intensity lasers lead to high third order NLO polarizabilities. The NLO properties of these 2D materials, particularly the nonlinear refractive index n₂ of them, need to be studied in detail. The third order nonlinear polarizability is an important parameter of nonlinear optical materials. Singh showed one phenomenon of changing the refractive index in the nonlinear photonic crystal [22]. There are many gauges to measure the third order nonlinear polarizabilities of materials [23–25], including interference method [26], nonlinear elliptical polarization method [27], third harmonic method [28], three wave mixing method [29], optical Kerman method [30] and wave front analysis method [31]. The Z-scan technology was first investigated by Sheik Bahae, et al. [32,33] in 1989. On the basis of spatial light beam distortion principle, a simple measurement technique can be used to measure the numerical value and the symbol of non-linear refractive index with a single beam. Due to its simple optical path, an easy measurement and powerful function, called Z-scan techniques have been used to measure the linear absorption coefficient, and nonlinear refraction coefficient of the materials [33,34]. The third order nonlinear polarizability of the materials is confirmed by measuring the transverse distribution distortion of Gaussian beam in nonlinear materials. The Spatial self-phase modulation (SSPM) method was used to investigate the NLO properties of 2D materials [24]. The Z-scan mechanism is self-focusing or self-defocusing, which is Gaussian beam, and SSPM mechanism and it is based on self-diffraction which is a concentric circle [35].

The nonlinear refractive index n₂ of the new 2D material GeSe suspensions is calculated by using SSPM method and Z-scan technique. Moreover, the third order nonlinear polarizabilities of the samples are also calculated by SSPM method. The different concentrations of GeSe nanoflake suspensions are produced by liquid phase exfoliation method and the characterization method of the samples were summarized. The effect of concentration on nonlinear refractive index n₂ is studied by Z-scan and SSPM. Then the instrument block diagram of the experiment is acquainted. The image of SSPM effect is presented in multiband, and the numerical values n₂ and χ⁽³⁾ of GeSe are calculated by experimental analysis at 532 nm laser wavelength. Nonlinear all-optical switching equipment is designed and united in SXPM based information transmission system.

2. Experiments methods and schemes

2.1. Preparations of GeSe nanoflake suspensions

The experiments for the 2D GeSe dispersions were performed by liquid phase exfoliation method. The GeSe interlayer Van der Waals’ force is overcome with ethanol solvent or surfactants mixed with GeSe. We obtain the GeSe dispersions after the removal of centrifugal removing GeSe block from the single layer, double layers, multiple layers GeSe and less GeSe block mixed suspensions. The experimental setup is shown in Fig. 1. and the details information are written in the previous work [36].

Fig. 1 Preparation of GeSe nanoflake dispersions by liquid phase exfoliation method.

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2.2. Characterization of the few-layer GeSe nanoflakes

The bedded structure of GeSe nanoflake is shown in Fig. 2(a). The GeSe dispersion liquid drops to the ultra-thin copper network, and after being dried, it is observed by TEM. TEM technique is more precise in the characterization of the morphology of the material, and can observe the overall feature of the sample and the number of layers of the sample. Moreover, it can also observe the lattice texture inside the sample by the high-resolution TEM (HRTEM) shown in Fig. 2(b). The observed inter distances of the lattice fringes were found to be 0.286 nm.

Fig. 2 Characterization of GeSe nanoflakes (a) GeSe architecture, (b) TEM image spectra, and HRTEM image, (c) Raman, (d) AFM image, and (e) Transmittance spectrums.

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As shown in Fig. 2(c), the Raman spectrum of GeSe nanoflake suspension represents broad bands with the peak maxima at 147 cm⁻¹ for B¹_3g, and 183 cm⁻¹ for Ag¹. The GeSe thin film morphology is characterized by AFM, as shown in Fig. 2(d). From two monolayers space is 0.542 nm [2] and GeSe thin-film heights of 1.43 nm, 2.98 nm, 3.54 nm and 3.79 nm, respectively, we can conclude the layer numbers as three to seven.

Transmittance spectrums measuring wavelength from 350 nm to 1200 nm are shown in Fig. 2(e). We measured the GeSe nanoflake samples for four different concentrations in three thickness cuvettes 1 mm, 5 mm and 10 mm, respectively and we investigated that transmissivities of GeSe nanoflakes are in the range of 2.20% to 99.80%, the absorptions are larger near the infrared band. Figure 2(e)① is cuvette thickness for 1 mm and concentrations are 0.1 mg/ml, 0.2 mg/ml, 0.5 mg/ml and 1.0 mg/ml, and as the concentrations increase, the transmittance changes decrease. Figure 2(e)② is concentration 0.1 mg/ml, cuvette thickness for 1 mm, 5 mm, and 10 mm, respectively and the thicknesses of cuvette become thicker, the transmittance changes get lower. Figure 2(e)③ is the transmittance for all the GeSe suspensions in different concentrations and different cuvette thicknesses.

3. Results and discussions

3.1. Z-scanning measure the Kerr nonlinearity of 2D GeSe

The closed hole Z-scan method to measure the nonlinear Kerr effect of the material, and the experimental device is shown in Fig. 3. For the convenience of calculation, the 5:5 spectroscopes are chosen for the experiment, the transmitted light intensity is partly received by the detector 1 as reference, and the other part is obtained by the detector 2 (closed hole probe) after the light beam passed through lens, samples, and aperture. In the experimental process, the power of the incident laser is kept fix and the sample is moved in front and back of the lens focal point along the direction of light propagation. By changing the size of the spot incident to the sample, the sample experiences different light intensities. The power of the probe at the z position of each step is recorded and the corresponding transmittance is obtained. For the convenience of experiment, the laser of suitable intensity is obtained after the incident excited light pulse passes through the attenuator (attenuation). A wavelength of 532 nm continuous wave (CW) laser beam is incident perpendicular to the sample after focusing by the lens.

Fig. 3 The schematic diagram of the Z-scan measuring device.

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The prepared GeSe suspensions in these Z-scan experiments are uniform in order to reduce the error rate. The incident light intensity in our experiment is very small, and no higher-order nonlinear effect is produced in our experiment.

It is assumed that Gaussian beam is the incident beam and its propagation is along the Z direction. The electric field displayed as

E (z, r, t) = E_{0} (t) \frac{ω_{0}}{ω (z)} \exp (- \frac{r^{2}}{ω {(z)}^{2}} - \frac{i k r^{2}}{2 R (z)}) e^{- i φ (z, t)},

where E₀(t) represents the electric field intensity at the focal point,

ω (z) = ω_{0} {(1 + z^{2} / z_{0}^{2})}^{1 / 2}

denotes the spot size of the light source at z position, and

z_{0} = k ω_{0}^{2} / 2

is the diffraction length of the laser.

R (z) =z (1 + z_{0}^{2} / z^{2})

is the curvature radius of the wave front at z,

k = 2 π / λ

denotes the wave vector, φ is the phase of the beam propagating in the medium, and the intensity of the excited light can be expressed as,

I (z, r, t) = I_{0} (t) \frac{ω_{0}}{ω {(z)}^{2}} \exp (- \frac{2 r^{2}}{ω {(z)}^{2}}) .

If the thickness of the sample is less than the diffraction length, the phase change of the laser can be expressed as

\frac{\partial φ}{\partial z'} = k n_{2} I .

And the change in strength is expressed as

\frac{\partial I}{\partial z'} = - α (I) I .

For the Eq. (4) integral into (3), the integral is obtained.

Δ φ (z, r, t) = \frac{Δ φ_{0} (t)}{1 + \frac{z^{2}}{z_{0}^{2}}} \exp (- \frac{2 r^{2}}{ω {(t)}^{2}}),

in which the light beam ∆φ₀ is the phase change amount of the light beam at the focal point, which can be represented by the light intensity level I₀ at the focal point, that is,

Δ φ_{0} (t) = k n_{2} I_{0} (t) L_{e f f},

_{$L_{e f f} = \frac{1 - e^{- α_{0} L}}{α_{0}}$} is the effective distance of the beam in the sample.

The beam electric field through the sample can be expressed as

E_{a} (z, r, t) = E (t) e^{- \frac{α_{0} L}{2}} e^{- i Δ φ (z, r, t)} .

Using Gaussian decomposition method, Sheik-Bahae et al decomposed the exponent of the equation by Taylor series, and replaced the complex electric field at the small hole with several independent Gaussian beams, simplified the Eq. (7), and obtained the integral. When

| Δ φ_{0} (t) | ≪ 1

,

d ≫ z_{0}

, x = z/z₀, after a series implification of the equations, the normalized transmittance curve obtained by Z-scan measurement can be fitted with the following equation:

T (x) = 1 - \frac{4 Δ φ_{0} x}{(1 + x^{2}) (9 + x^{2})} .

In the actual experiment, we use the Eq. (8) to fit the curve obtained by Z-scan, get ∆φ₀ and bring it into Eq. (6), we can get nonlinear refractive index value n₂.

In Fig. 4, the normalized transmittances of the four concentrations of GeSe suspensions are expressed as a function of sample position in closed Z-scan by using 1 mm cube sample unit. As they can be seen from Fig. 4, each curve has a pre-focal peak then a post-focal valley, revealing that the nonlinear refractive index n₂ is negative, and this is self-defocusing. The thermal absorption process creates a spatial temperature distribution in the medium. Thus, in the analysis of the closed z-scan measurement, the non-local interaction between the radiation light and the sample is taken into account [37]. The nonlinear refractive index n₂ values of 0.1 mg/ml, 0.2 mg/ml, 0.5 mg/ml and 1.0 mg/ml concentrations of GeSe suspensions are calculated by using Eq. (8) with the closed hole normalized transmittance data showing in the Fig. 4, and listing in Table 1. As shown in Table 1, the sample of 1.0 mg/ml concentration shows the maximum nonlinear refractive index in these four concentrations. This could be the fact that the number of molecules of 1.0 mg/ml concentration per unit volume is higher than that of the other three concentrations, the absorption coefficient is the highest, and absorb more power from the laser beam, resulting in more heat. Because the nonlinear origin of the studied samples is thermal and non-local, the nonlinear refraction of the samples with 1.0 mg/ml concentration is higher than that of the other three concentrations [38].

Fig. 4 The closed hole Z-scan measurement results of the GeSe nanoflakes.

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Table 1. Nonlinear properties of GeSe by Z-scan Experiment

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In the actual Z-scan measurement, the curve of nonlinear refraction coefficient usually contains nonlinear absorption characteristics, such as nonlinear saturation absorption or multiphoton absorption, all of which have an effect on the measurement results. The entire curve is no longer symmetrical. To this end, a typical closed hole measurement curve is obtained, and the effect of the nonlinear absorption characteristic is eliminated, and only the influence of the nonlinear absorption needs to be removed. The obtained closed hole Z-scan test curve is split by the open hole Z-scan test curve, and the resulting curve is caused by the Kerr effect of the material [39,40].

3.2. SSPM method for measuring Kerr nonlinearity of 2D GeSe

The nonlinear optical property measurements are taken with the device showing in Fig. 5. The 532 nm wavelength CW laser is using as a light source passed through the polarizer and focused behind the lens (focal length 200 mm), then is dispersive through GeSe nanoflake suspensions which filled in 1mm, 5mm, and 10 mm quartz cuvettes, respectively. The phase shift produced by CW laser excites the SSPM effect through GeSe dispersion and diffracts into the diffraction ring. The diffraction ring patterns can be obtained from a charge-coupled device produced by coherent imaging or from a black screen suspended behind a sample quartz cuvette.

Fig. 5 The schematic diagram of the SSPM measuring device

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The results show that the diffraction ring patterns are distorted rapidly after the incident CW laser beam passes through the GeSe suspensions horizontally. When the CW laser beam wavelength of 532 nm passes through GeSe suspended object, the diffraction pattern starts from a small circle and quickly turns into a series completely symmetric concentric ring, and then the diffraction ring begins to distort rapidly, so as to obtain a stable collapse pattern. The upper part of the diffraction ring collapses toward to the center of the ring, and the button part of the ring remains nearly full circle, forming a semicircular diffraction ring. It is very obviously of the collapse in the vertical direction. The closer to the external collapse in the top half of the ring, the more obvious the collapse effect will be. This phenomenon is known as the collapse effect of the diffraction ring in SSPM. Collapse effect plays a crucial role in studying the variety of nonlinear refractive index n₂ of materials. The change of refractive index n₂ of the 2D materials caused by laser intensity can be gauged by this collapse effect [41].

Collapse deformation has evident light intensity and regularity, all of which display linear variation. The magnitude of the upper collapse can be described in terms of the angle from the sample to the pattern formation shown in Fig. 6(a). When the diffraction ring appears, a range of concentric cones are shaped in the spatial diffraction path. The angle from the maximum cone axis to the cone side is the semi-cone angle, that is, the collapse distance from R_D, to the maximum semi-diffractive angle θ_H, and the maximum diffraction radius R_H. D is the distance between sample and mode. In the case of D >> R_H, this relationship can be explained as

θ_{H} = \frac{R_{H}}{D} .

After the diffraction ring collapses stably, the maximum half angle of the upper part of the diffraction pattern is θ_H, and the maximum radius of diffraction is R′_H. If D >> R′_H, then the equation is as follows

Fig. 6 (a) Distortion principle diagram of GeSe nanoflake dispersion; (b), (c) change of the distortion angle (θ_D) and the the maximum semi-diffractive angle (θ_H) with the incident intensity increasing; (d) variation in the nonlinear refractive index of GeSe after distortion.

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{θ^{'}}_{H} = \frac{{R^{'}}_{H}}{D} .

The distortion angle and distortion diffraction radius are defined as θ_D and R_D, on the basis of R_D = R_H - Rʹ_H, the relationship between them can be displayed as

θ_{D} = θ_{H} - {θ^{'}}_{H} = \frac{R_{D}}{D} .

The maximum half angle of diffraction pattern can be calculated using equation

θ_{H} = \frac{λ}{2 π} {(\frac{d Δ ψ}{d r})}_{\max} .

Equation (12) could be shortening as the next equation for a Gaussian beam

θ_{H} = n_{2} I C,

C = {[- \frac{8 r L_{e f f}}{ω_{0}^{2}} \exp (- \frac{2 r^{2}}{ω_{0}^{2}})]}_{\max},

if r is a constant, the distortion angle θ_D can be written as follow

θ_{D} = θ_{H} - {θ^{'}}_{H} = (n_{2} - {n^{'}}_{2}) I C = Δ n_{2} I C .

Finally from Eqs. (13) and (15), the relations of the relative variable of nonlinear refractive index and the distortion angle θ_D and the maximum semi-diffractive angle θ_H is obtained by eliminating the maximum semi-diffractive angle constant

Δ n_{2} / n_{2} = θ_{D} / θ_{H} .

The change of the maximum semi-diffractive angle (θ_H) and the distortion angle (θ_D) with the incident intensities variety in 532 nm wavelength, from diffraction patterns are obtained by CCD, shown in Fig. 6. The variation rates of nonlinear refractive index as shown in Fig. 6 are obtained from calculation.

With the increase of intensity, the maximum semi-diffraction angle (θ_H) and distortion angle (θ_D) in CW 532 nm are close to linear variation. The results show that the distortion will cause great changes in the nonlinear refractive index in the dispersion of several layers of GeSe nanoflakes. Therefore, the relative variation of GeSe suspensions nonlinear refractive index can be got through the ratio of the distortion angle (θ_D) to maximum semi-diffractive angle (θ_H) in the measurement shown as θ_D/θ_H. This means that the relative variation of nonlinear refractive index varies with the change of light intensity. With the increase of light intensity, the change of light intensity is monotonous. That is to say, the larger the incident intensity, the more obvious the collapse, and the larger the change of nonlinear refractive index, this is in accord with the observed collapse effect.

The effect of GeSe suspension concentrations in the measurement results has been investigated in Fig. 6. The widths of the colorimetric dishes are set as 1 mm, 5 mm and 10 mm, respectively, and then the concentrations of GeSe suspensions were changed. θ_D, θ_H, and θ_D/θ_H values are increasing by the light intensity increased from 4.17 W/cm² to 91.93 W/cm², and the θ_D, θ_H, and θ_D/θ_H values higher when the concentrations are higher with the same thickness of the colorimetric dish.

The effect of the width of the colorimetric dish in the measurement was then investigated. The widths of the colorimetric dish are different, namely 1mm, 5mm and 10mm, respectively, while the concentrations of the prepared sample for each group data are the same, and four different concentrations are prepared. θ_D, θ_H, and θ_D/θ_H values of GeSe were determined by the self-phase modulation method. From data in Fig. 6, θ_D, θ_H, and θ_D/θ_H values are increasing by the light intensity increased from 4.17 W/cm² to 91.93 W/cm², and the θ_D, θ_H, and θ_D/θ_H values higher when the width of the cuvette are higher in the same concentrations of GeSe. Finally, the third-order nonlinear polarizability of GeSe under four concentrations and three width colorimetric dishes were listing in Fig. 6.

Through the change of refractive index caused by the light field of GeSe, some famous optical phenomena like self-focusing and self-phase modulation have been produced. According to Kerr's law, the change of light intensity is going to change the refractive index to produce a phase shift (Δψ) [42,43].

Δ ψ = \frac{2 π n_{0}}{λ} \int_{0}^{L_{e f f}} n_{2} I (r, z) d z,

where L_eff is an effective optical propagation length, λ is the wavelength, I(r, z) is the intensity distribution and r is the radial position. The refractive index can be written as follow [44].

n = n_{0} + n_{2} I,

n₀ and n₂ are the linear and nonlinear refractive indices, and I stands for the incident intensity. The effective thickness of the quartz cuvette is

L_{e f f} = {\int_{L_{1}}^{_{L_{2}}} (1 + \frac{z^{2}}{z_{0}^{2}})}^{- 1} d z = z_{0} a c r \tan (\frac{z}{z_{0}}) | \begin{matrix} L_{2} \\ L_{1} \end{matrix},

where z is the propagation, and length z₀ is the Rayleigh length. The nonlinear refractive index n₂ of GeSe suspension is abbreviated as [45]

n_{2} = \frac{λ}{2 n_{0} L_{e f f}} \cdot \frac{N}{I} .

As a result of the slope of the ring numbers and intensities, χ⁽³⁾_total of the GeSe nanoflakes could be written as

χ_{total}^{(3)} = \frac{c λ n_{0}}{2.4 \times 10^{4} π^{2} L_{e f f}} \cdot \frac{d N}{d I} .

The relationship between the third-order nonlinear polarizability χ⁽³⁾_total of the whole GeSe dispersion and the third-order nonlinear polarizability of the GeSe monolayer χ⁽³⁾_monolayer can be explained as

χ_{total}^{(3)} = χ_{m o n o l a y e r}^{(3)} N_{eff}^{2},

where N_eff is the effective amount of monolayer.

In Fig. 7, we clearly see the diffraction ring numbers varying with different widths of quartz cuvettes and different concentrations, showing linear relationship between them. The research was extended to higher GeSe concentrations. After reaching a specific threshold concentration, the GeSe completely blocks the intense laser. For 5 mm cuvette, threshold concentration is 1 mg/ml, and for 10 mm cuvette, threshold concentration is 0.5 mg/ml. The incident intensity with a slope of dN/dI, the nonlinear refractive index n₂, the effective amount of monolayer N_eff and the third-order nonlinear polarizability are listed in Table 2.

Fig. 7 The diffraction ring numbers of different concentration GeSe nanoflake suspensions received by CCD varying with the incident intensities at wavelength of 532 nm.

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Table 2. Nonlinear properties of GeSe by SSPM Experiment

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Therefore, the nonlinear refractive index n₂ of the corresponding GeSe suspensions can be obtained by solving the linear relationship between the numbers of bright stripes and the incident light intensities. When the width of cuvettes and the concentrations of GeSe are changed, the numbers of bright stripes are always linearly related to the intensities of incident lights. By solving the slope of the fitting line in the diagram, the nonlinear refractive index n₂ of GeSe dispersion is shown in Table 2. It is shown that the refractive index measured by this method is in the order of 10⁻⁶ m²/W and 10⁻⁶ esu for the third order nonlinear polarizabilities χ⁽³⁾. The results display that the widths of cuvettes and the concentrations of GeSe suspensions have little effect on the effective nonlinear refractive index and the third order nonlinear polarizabilities, but the values of monolayer GeSe changed a lot in pace with N_eff which determined by the widths of cuvettes and concentrations. The data indicate that the nonlinear refractive index measured by the SSPM method is reliable when the N_eff is determined.

According to the theoretical results, it can be solved experimentally. In order to verify the reliability of the method in measuring the nonlinear coefficient, the third-order nonlinear polarizabilities of GeSe with different concentrations and in different thickness of cuvette have been calculated. The effects of the widths of the cuvettes on the measurement were first investigated. The concentrations in the prepared sample are the same, and the widths of the cuvettes are different, namely 1 mm, 5 mm and 10 mm, and the third order nonlinear polarizabilities of the GeSe suspensions are determined by the SSPM method. From data in Table 2, the third order nonlinear polarizabilities χ⁽³⁾_total of GeSe is on the order of 10⁻⁶ esu, and along with the widths of the cuvettes increase from 1mm to 10 mm, the N_eff increase and then followed the values of monolayer GeSe χ⁽³⁾_monolayer decrease.

The effect of the concentrations of GeSe on the third order nonlinear polarizabilities can be obtained, and when the widths of the cuvettes are set the same, to change the concentrations of GeSe suspensions, the third order nonlinear polarizabilities of the GeSe are effectively calculated by using the SSPM method. From data in Table 2, the third-order nonlinear polarizability χ⁽³⁾_total of GeSe is on the order of 10⁻⁶ esu, they have little effect with widths of the cuvettes and concentrations. But along with the concentrations increase, the N_eff increase and then followed the value of monolayer GeSe χ⁽³⁾_monolayer decrease.

In the equation, χ⁽³⁾_total is the effective third order nonlinear polarizability of the whole GeSe dispersion. We can find out the χ⁽³⁾_total, but the numbers of GeSe layers have great influence on the χ⁽³⁾_monolayer. Different GeSe dispersions have different GeSe layers, so the corresponding χ⁽³⁾_monolayer is very different. Therefore, the effective third order nonlinear polarizabilities of the whole GeSe dispersions have no practical physical significance. It is certainly worth solving the third order nonlinear polarizabilities of GeSe monolayer χ⁽³⁾_monolayer.

Finally, the third order nonlinear polarizabilities of GeSe suspensions under different concentrations and the width of the same cuvette were investigated listing in Table 2. To sum up, changing the widths of the cuvettes and the concentrations of GeSe suspensions have no significant effect on the results of third-order nonlinear polarizabilities χ⁽³⁾_total which are all in the range of 10⁻⁶ esu. And the third order nonlinear polarizabilities of monolayer χ⁽³⁾_monolayer GeSe have a certain difference from 10⁻⁷ esu to 10⁻¹⁰ esu, due to the effective amount of monolayer N_eff increasing. It can be concluded that the spatial self-phase modulation method is a simple and effective method to study the nonlinear properties of layered materials.

From the above results, the nonlinear refractive index n₂ of GeSe dispersions nearly stay in the order of 10⁻⁶ cm²/W for SSPM, which is different from the result in the order 10⁻⁹ cm²/W for Z-scan technique, for the same sample. These differences are attributed to the level of incident light intensities used in both methods and the thermal lens effects and intrinsic nonlinear optical excited by a strong CW laser. The incident light intensities for SSPM methods are 4.178~91.934 W/cm² to excite diffraction rings, while for Z-scan it was 0.678 W/cm² to keep the light as a Gaussian beam to avoid higher order nonlinear effects. And from the previous work about thermal lens and intrinsic nonlinear optical all have big effect of them [46,47]. It is also known that the refractive index is intensity dependent.

Here we cite the data of 10 mm cuvette width and concentration 0.1 mg/ml sample measured in SSPM as compare with other 2D materials are listed in Table 3 [48–50].

Table 3. n₂ and χ⁽³⁾_monolayer for a variety of 2D materials.

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4. Application of GeSe nanoflakes: all-optical Information conversion

The schematic diagram of the experimental configuration presented in Fig. 8 is an optical controlled optical technique based on GeSe SXPM effect. CW 671nm controlled light was used to modulate / manipulate 532nm to control the transmission of light, and the optical switch of GeSe nanoflake dispersion was realized. The controlling light and the controlled light are kept at the same level and placed in the 1mm thick quartz container through the GeSe nanoflake dispersion. The intensity of the two lights changes by attenuating slices, focusing on the center of the small square by focusing the 200 mm lens. By increasing the incident intensity of controlled light, the nonlinear phase in GeSe suspensions can be changed. When the laser beam passes through the lens and samples, we can get the diffraction rings on the white screen.

Fig. 8 Schematic of the experimental configuration for all-optical switching and all-optical information conversion.

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All-optical information conversion is a kind of information conversion from one wavelength channel to another wavelength channel using optical control technology. The signal light phase can be emphasized by the incident light of the controlling light. The input information is used to address the control light, and the optical information transmission from the control light to the signal light is realized. The signal light output information is analyzed and the identical objective information is obtained. Figure 8 shows the all-optical switching device configuration. The on/off state of the laser beam is controlled by a baffle. The laser beam is divided into two same optical power sections when it passes through the BS, one beam of the lights is detected on the electric detector 1. Then an aperture is arranged at the outermost diffraction ring of the signal light, and the transmitted light is detected by the detector 2. The laser 2 (532 nm) is the signal light, and the diffraction ring of the signal light is reconstructed by the laser 1 (671 nm).

The signal light diffraction ring cannot be further excited while the baffle is closed, and becomes the green spot of the Gaussian laser beam. At this point, detector 2 cannot be able to detect any optical signals. However, when the bezel is opened, the diffraction ring of the signal light will be retransmitted and the transmitted light will be received by the detector 2. With this nonlinear effect, an all-optical information transmission and conversion system to transmit/convert information can be designed. We leave the border at 4 s, and then close another 4 s. Using the same program four times, we can get signals from detector 1, as shown in Fig. 9(a)①. At the same time, as shown in Fig. 9(a)②, we can receive the output signal from detector 2. It needs to be careful that the dispersion ring of the signal light changes after the signal light is about ≈0.8s, so when the signal light is received, there is a delay of about ≈0.8s in the detector 2.

Fig. 9 (a) The signal received from detector 1 (① 671 nm controlling light) and detector 2 (② 532 nm signal light), (b) ① is the input signal of the ASCII code of “I ♥ S Z” and ② is the identical output signal.

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Figure 9(b) shows a specific example of transmission information. Through control the baffle, we can transmit an input signal “01001001 00000011 01010011 01011010”, which is the ASCII code of “I ♥ S Z” of the controlling light. Meanwhile, an output signal “I ♥ S Z” can be copied (Fig. 9(b)②). This study supply a new way of optical communication technique development. We can foresee that the transformation of heterotopic information will have a positive impact on communication technique.

5. Laser/2D GeSe interaction mechanism

The direct band gap value of GeSe was determined to be 1.37 eV [51] by using 532 nm and 671 nm laser as light source to interact with GeSe, shown in Fig. 10. Because of the Kerr effect, the reflection index of GeSe dispersion varies with the incident intensity. During the Gaussian lights pass through the GeSe samples, the phase shifts of the light (Δψ) can be explained by the following equation [52]

Δ ψ = \frac{2 π n_{0}}{λ} \int_{0}^{L_{e f f}} n_{2} I (r, z) d z, r \in [0, + \infty),

where r and I (r, z) characterize radial coordinates and intensity distribution of incident light severally. These two points have the same wave vectors to generate the disturbance, and the light and dark streaks can be definitized as follows

Fig. 10 The band gap structure which allows free carrier wide spectrum excitation and the mechanism of light interacting with several layers of GeSe.

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Δ ψ (r_{1}) - Δ ψ (r_{2}) = M π (M is an integer)

Odd values of M cause dark fringes and even values of M cause bright fringes. This is the SSPM phenomenon, from [Δψ(0) − Δψ(∞)] = 2Nπ to get ring numbers (N). The SXPM, pumped light affects the nonlinear refractive index of GeSe dispersions, and the probe light will lead to additional phase transitions, thus triggering additional diffraction rings. The nonlinear optical response can be interpreted as the arrangement and reorientation of GeSe dispersion brought by electromagnetic field [53], which is similar to liquid crystal.

6. Conclusions

Diverse concentrations of GeSe ethanol dispersions were produced by the method of liquid phase exfoliation and followed by characterized with Raman, TEM, and AFM etc. The nonlinear refractive index n₂ and the third-order nonlinear polarizabilities χ⁽³⁾ of GeSe were experimentally verified in the 532 nm CW laser by Z-scan method and SSPM effect. The nonlinear refractive index n₂ of GeSe dispersions basically stay in the order of 10⁻⁹ cm²/W for Z-scan methods and in the order of 10⁻⁶ cm²/W for SSPM. Each curve of Z-scan has a pre-focal peak and a post-focal valley for closed hole trace because the transmittance of the sample at the focal point decreases. The diameter, brightness and diffraction ring number augment with the increase of incident light intensities, showing the distribution characteristics of outer strong inner weak, external thick inside thin. Diffraction rings will collapse with the passage of time, and reach the stability of pattern after a period of time. Based on these characteristics of nonlinear optical response and high stabilities of GeSe, an all-optical switch based on GeSe was proved. GeSe has many advantages like rich properties, high stability, high nonlinear response, and narrow band gap. It is supposed to be applied in optical devices such as all-optical information conversion in the foreseeable future.

Funding

National Natural Science Foundation of China (11874269, 61875133, and 11775147); Science and Technology Project of Shenzhen (JCYJ20180305125036005, JCYJ20180305124842330, and JCYJ20180305125443569); Guangdong Natural Science Foundation (2018A030313198); China Postdoctoral Science Foundation (2017M622746 and 2018M633129).

Disclosures

There are no conflicts to declare.

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Thickness	Concentration	n₂
		× 10⁻⁹ (cm²/W)
1mm	0.1	1.307
	0.2	7.995
	0.5	8.129
	1.0	9.627

Thickness	Concentrations	dN/dI	n₂	χ⁽³⁾	N_eff	χ⁽³⁾_monolayer
			× 10⁻⁶ (cm²/W)	× 10⁻⁶ (esu)		(esu)
1mm	0.1	0.047	9.212	4.297	4	2.366 × 10⁻⁷
	0.2	0.071	13.19	6.492	8	8.113 × 10⁻⁸
	0.5	0.106	20.777	9.692	21	2.076 × 10⁻⁸
	1.0	0.121	23.717	11.064	46	5.123 × 10⁻⁹
5mm	0.1	0.151	5.919	2.761	22	5.710 × 10⁻⁹
	0.2	0.171	6.703	3.127	44	1.597 × 10⁻⁹
	0.5	0.230	9.016	4.206	107	3.607 × 10⁻¹⁰
10mm	0.1	0.236	4.625	2.158	43	1.166 × 10⁻⁹
10mm	0.2	0.247	4.841	2.258	87	2.945 × 10⁻¹⁰

Thickness	Concentration	n₂
		× 10⁻⁹ (cm²/W)
1mm	0.1	1.307
	0.2	7.995
	0.5	8.129
	1.0	9.627

Thickness	Concentrations	dN/dI	n₂	χ⁽³⁾	N_eff	χ⁽³⁾_monolayer
			× 10⁻⁶ (cm²/W)	× 10⁻⁶ (esu)		(esu)
1mm	0.1	0.047	9.212	4.297	4	2.366 × 10⁻⁷
	0.2	0.071	13.19	6.492	8	8.113 × 10⁻⁸
	0.5	0.106	20.777	9.692	21	2.076 × 10⁻⁸
	1.0	0.121	23.717	11.064	46	5.123 × 10⁻⁹
5mm	0.1	0.151	5.919	2.761	22	5.710 × 10⁻⁹
	0.2	0.171	6.703	3.127	44	1.597 × 10⁻⁹
	0.5	0.230	9.016	4.206	107	3.607 × 10⁻¹⁰
10mm	0.1	0.236	4.625	2.158	43	1.166 × 10⁻⁹
10mm	0.2	0.247	4.841	2.258	87	2.945 × 10⁻¹⁰

Kerr Nonlinearity in germanium selenide nanoflakes measured by Z-scan and spatial self-phase modulation techniques and its applications in all-optical information conversion

Abstract

1. Introduction

2. Experiments methods and schemes

2.1. Preparations of GeSe nanoflake suspensions

2.2. Characterization of the few-layer GeSe nanoflakes

3. Results and discussions

3.1. Z-scanning measure the Kerr nonlinearity of 2D GeSe

3.2. SSPM method for measuring Kerr nonlinearity of 2D GeSe

4. Application of GeSe nanoflakes: all-optical Information conversion

5. Laser/2D GeSe interaction mechanism

6. Conclusions

Funding

Disclosures

References

Cited By

Figures (10)

Tables (3)

Equations (24)

Optics Express

2D materials	wavelength	n₂	χ⁽³⁾_monolayer	References
	(nm)	(cm²/W)	(esu)
Grephene	473	10⁻⁷	10⁻⁷	Ref [48]
Grephene	532	10⁻⁷	10⁻⁷
BP	350	10⁻⁵	10⁻⁸	Ref [49]
BP	600	10⁻⁵	10⁻⁸
MoS₂	488	10⁻⁷	10⁻⁹	Ref [25]
NbSe	532	10⁻⁵	10⁻⁹	Ref [50]
	671	10⁻⁵	10⁻⁹
GeSe	532	10⁻⁶	10⁻⁹	This work