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Abstract
Regular arrangement of dispersed 2D flakes, as the “Wind-Chime” model, has been regarded as possible mechanism of spatial self-phase modulation. But this regular arrangement caused by the laser have not been confirmed, and the relation with the concentration of dispersed 2D flakes is still unclear. Here, the relationship between arrangement caused by electric field and polarized transmittance have been explored at first. Then, the model of flakes rotation to regular arrangement were established, which were proof by the response time by turning on/off electric field. On this basis, by building the polarization-related cross optical switch system, light-induced regular arrangement were observed and proven.
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1. Introduction
Diffraction rings could be induced, when focusing the laser on the surface of 2D flakes dispersion such as Graphene Oxide (GO) [1] and Black Phosphorus [2], which is called spatial self-phase modulation (SSPM). SSPM has been widely reported in 2D Te [3], topological insulator Bi2Te3 [4], MXenes [5] and different materials [6–8], which has been used in optical switch [1], optical heterostructure [9–11] and measuring nonlinear refractive index n2 [12–14]. But its formation mechanism has not been confirmed yet. The strongest hypothesis is the Wind-Chime model [15] that 2D flakes are arranged regularly in solution, thus causing nonlocal ac electron or hole coherence [16,17]. This hypothesis was indirectly proof by the relationship between the number of active flakes and saturated intensity as reported in Photonics Res [18]. However, regular arrangement of nanosheets induced by light field have not been observed directly yet.
Electric field induced regular arrangement of GO nanosheets could modulate the transmittance of polarized light. In 2014, Nat. Mater. reported the electric field induced birefringence of GO nanosheets (GONS) in 2D flakes [19]. After that, the effect of sizes are also explored [20], then other 2D electric field induced birefringence materials are reported such as Zirconium Phosphate (ZrP) [21] and Black Phosphorus (BP) [22]. As reported in those papers, their transmittances over orthogonal polarizers are increased efficiently by applying large electric field (E), it is due to their increasement of regular arranged nanosheets in dispersion. But when applying extremely large electric field, their transmittance will be reduced after increasement, because of the irregular arrangement caused by the thermal convection. The relationship between transmittance of polarized light and regular arrangement needs to be studied quantificationally.
In this study, the alignment factors of 2D flakes under electric field have been quantificationally discussed. Then the polarization-related cross optical switch system was designed and built. By applying near infrared femtosecond pulsed laser to induce SSPM, the Wind-Chime model induced by laser were observed directly by birefringence.
2. Results and discussion
2.1 Relationship between arrangement and polarized transmittance
The relationship between regular arrangement of nanosheets and the polarized transmittance could be observed and measured as similar with measurement of electric field induced birefringence [19,20]. The experimental setup is shown in Fig. 1(a). The light sources are LED (AIJPPV, AP-XD-E1014J) or 543 nm laser (REO, Model. 33361). The polarized transmittance is defined as the transmittance over samples with a pair of orthogonal polarizers, which could be detected by photo detector (Thorlabs, S120VC).
Fig. 1. a) Rotation of polarized light after regular arranged nanosheets; b) scanning electron microscopy (SEM) image; c) force analysis of nanosheets when the electric field (E) is applied; d) Macroscopic photos of low (0.833 mg/mL) and high (1.333 mg/mL) concentration black phosphorus (BP) dispersions.
Black Phosphorus nanosheets (BPNS), as an electro-optical polarization conversion material reported recently [23], were chosen for this research. With anisotropic atomic structures [24–26], relative permittivity around 5.76 [27–29], they have high conductivity, which is higher than GO [30–33], and their fast carrier mobility around 10000-26000 cm2V-1s-1 [24,34,35], high on-off current ratio [36,37], excellent photothermal properties [38,39]. Their thickness-dependent structural stability [26] also endow them characters different with other 2D materials. These chosen BPNS dispersed in N-methyl-2-pyrrolidone (NMP), as scanning electron microscopy image shown in Fig. 1(b), their average diameters are around 2.6 ± 0.7 µm and average thickness are less than 2 nm, was reported in detail in previous paper [22] and negligible in their response time.
The regular arrangements of BPNS are controlled by applying a horizontal electric field (E) to dispersion. Benefited from their different effective electron mass along to two directions [40–42], carriers inside BPNS are polarized, resulting in different forces at two ends. As shown in Fig. 1(c), with sum of rotation torque $|{\vec{M}} |= \left|{\smallint \vec{F} \times d\vec{r},} \right|$, nanosheets are rotated under E.
Rotated and regular arranged BPNS could rotate the polarization of polarized light. For single nanosheet, caused by its anisotropic structure, BPNS absorbs more light at armchair (AC) direction than zigzag (ZZ) direction, thus rotating the polarized direction of light [23]. By applying electric field (E), because the electron effective mass along AC direction is only 1/5 of ZZ direction [43], at the effect of isotropic Coulomb forces, with their sheeted morphology [24,44,45], carriers inside BPNS are easier to be moved along AC, which is also proved through that conductivity along AC is 2-3.5 times larger than it along ZZ [42,46,47]. So, after the polarization of carriers, electric forces are different at two ends of BPNS, thus the regular arrangement of BPNS dispersion are formed. Then, the rotation and intensity of polarized light over a pair of orthogonal polarizers and the BPNS dispersion is changed.
The polarized transmittance of 0.833 mg/mL BPNS dispersion (as low concentration) under the E = 30 V/mm are observed. By using white LED source, macroscopic photos without and with E are shown in Fig. 1(d)). After applying E, its transmittance increases and remains in the ‘on’ and ‘remain’ section. After removing E, the transmittance recovery back to initial value. But it will have different phenomenon at same condition as shown in Fig. 1(e) when increasing concentration to 1.333 mg/mL.
These phenomena could be measured quantificationally with the 532 nm light source as shown in Fig. 2(a), just like the electric field induced birefringence behaviors. The normalized intensity increases and keeps around 2.96 in the ‘on’ and ‘remain’ section, then fall quickly in the ‘off’ section.
Fig. 2. a) Normalized transmittances, b) arrangement of flakes and c) driving or resistance effects analysis of low concentration (0.833 mg/mL) black phosphorus (BP) dispersions and d-f) their corresponding differences after increasing concentration to 1.333 mg/ml.
Corresponding mechanisms could be explained as shown in Fig. 2(b). After applying E, most BPNS are arranged regularly along the electric field. Regular arranged nanosheets could rotate the linear polarized light into different direction and result in different polarized transmittance, similar with the report about GONS [19,20]. After removing E, BPNS became random arranged, so the polarized transmittance decrease. The quantificational relationship between the nanosheets’ regular arrangement in dispersion and the polarized transmittance will be discussed and researched further in third part, which have not been reported.
A dynamic model about the arranged nanosheet with or without E was established as Fig. 2(c). To simplify the model, BPNS are considered as a simply model with regular shapes like thin cylinder. When E is applied, the driving force for regular arrangement are electric force (FE) and the flow induced force (Ff) [19], the resistance are the friction (f) and effects from Brownian motion (b). After removing E, the driving force for random arrangement is effects from Brownian motion (b), while the resistances still are the friction (f). This model will explain the response time of nanosheets’ rotation in second part.
The nanosheets’ regular arrangement in dispersion will be influenced by the concentration and temperature. Figure 2(d) is the normalized transmittances of 1.333 mg/mL BPNS dispersion at same condition. After applying E, the normalized intensity increases to 3.33 in the ‘on’ section, but decreases and keep as 1.65 in the ‘reduce’ section. After removing E, it reduces rapidly to 0.48, then recover slowly in the ‘off’ section.
Corresponding explanations are shown in Figs. 2(e,f). The larger maximal transmittance benefited from the more regular arranged nanosheets, whose flow induced force (Ff) is larger in higher concentration dispersion due to their larger viscosity [19]. The ‘reduce’ process mean that the nanosheets are arranged less regularly, caused by the accumulation of electric thermal convection, because of the lower resistivity, larger current of higher-concentration dispersion. After removing E at ‘off’ stage, BPNS are more irregular arranged caused by obvious thermal convection, then recover slowly with the dissipation of heat. So, the thermal convection (Q) cannot be ignored in the dynamic model of high concentration dispersion.
Comparing the steady-state in Fig. 2(a) and the non-steady-state in Fig. 2(d), it means that nanosheets in the ‘on’ section of the steady-state in Fig. 2(a) are not complete regular arranged, and nanosheets in the ‘off’ section are not complete irregular arranged. Thus, new model of regular arrangement and rotation are essential to be established.
2.2 Model of regular arrangement
By referencing Wind-Chime model in SSPM, a modified model is established and simplified. At ‘off’ stage, as shown in Fig. 3(a), BPNS are arranged randomly. By defining the θ as angle between long axis of BPNS and horizon, their arrangement could be simplified to a single BPNS with $\overline {\varDelta \theta } = \frac{{\mathop \sum \nolimits_{i = 1}^N \varDelta {\theta _i}}}{N} =\pi{/}4$ as shown in Fig. 3(b). At ‘on’ stage, by applying an appropriate horizonal E, as shown in Fig. 3(c), BPNS are regular arranged along electric field, resulting in an angle of 0 with E as shown in Fig. 3(d).
Fig. 3. Arrangement of nanosheets and their corresponding equivalent modified model at the stage of a,b) ‘OFF’ or c,d) ‘ON’; e,f) force analysis during the process of rotation; g) definition and formula of response time.
By applying E, BPNS are affected by two resultant forces with opposite directions at two ends, as shown in Fig. 3(e), it is rotated from $\theta =\pi {/}4$ to horizon ($\theta = 0$). Similarly, after removing E, BPNS are rotated back to their original state ($\theta =\pi{/}4$). Considering its final state, the resultant force at off state could be assumed as shown in Fig. 3(f), which is also $\pi{/}4$ with horizon at two ends of BPNS.
By defining ‘on’ time ton and ‘off’ time toff, which are collectively called as response time, as the time from 10% to 90% of variation between angle related maximal and minimal intensity during the variation as shown in Fig. 3(g). Imitating the derivation of rotating time in Wind-Chime model of SSPM [15], rotational torque is established in electric field induced birefringence model. Respond time could be derived (Supplement 1), whose relationship is
thereinto, η, viscosity coefficient, is 1.62 $m{m^2}/s$ for selected NMP solution at 25 °C, ξ represents the portion of solution rotating with nanosheet simultaneously, it is set to 0.1 in calculation [15], h is the thickness of nanosheets, which is set to be 0.82 nm for BPNS and 0.68 nm for the S-BPNS [22], whose variation of radius and thickness are negligible by even considering them as regular flakes, and $|{\vec{F}(R )} |$ is the radius-related resultant force, by substituting $|{\vec{F}(R )} |$ as resultant forces during the process of turning ‘on’ or ‘off’ electric field, the ‘on’ time and ‘off’ time could be derived and experimental data could be fitted by just changing the resultant force at ‘on’ stage or ‘off’ stage.Relationships between response times and E could be fitted and explained by modified model. For the dispersion of BPNS, whose SEM in discussed in S.I., with diameters around $2.5 \pm 0.5\;\mathrm{\mu}\textrm{m}$ and thickness around round $0.82\;\textrm{nm}$, as model shown in Fig. 4(a), their electric field induced birefringence are shown in Fig. 4(b), the response times could be calculated from it, as shown in Fig. 4(c). Thereinto, fitting lines (curves) match the experimental data (dots) well for both ton and toff, and by analyzing different parameter of fitting formula, it could be concluded that electric force (FE) and flow induced force (Ff) are the main driving force at ‘on’ stage, by contrast, the main driving force at the ‘off’ stage is Brownian motion (b).
Fig. 4. a) Model, b) electric field induced birefringence of BPNS and c) their corresponding response time are fitted over different electric field intensity (E); d-f) Model and verification of response time of S-BPNS.
To verify this model, submicron sized BPNS (S-BPNS) are introduced, as SEM shown in S.I., they have average diameters around $0.6 \pm 0.5\;\mathrm{\mu}\textrm{m}$ and thickness around $0.68\; \textrm{nm}$, whose model and electric field induced birefringence are shown in Figs. 4(d,e) respectively. With electric field induced birefringence better than BPNS, as shown in Fig. 4(f), measured response times (dots) of S-BPNS could also be fitted by formula (line). By comparing parameters of two sized nanosheets, FE and Q have more effects on rotation of BPNS, Ff have more effects on rotation of S-BPNS, which is consistent with conclusion before [22], that there are more carriers inside larger sized BPNS, it makes BPNS easier to be affected by FE. By contrast, smaller sized S-BPNS have larger friction (f) and Brownian motion (b), it is due to its smaller size and mass, and then S-BPNS are easier to be affected by friction and Brownian motion. Thus, conclusion could be gotten that by minishing size, FE and Q could be reduced efficiently, and f and b have more effects on their rotation.
By modified model, the dynamic between random ($\theta =\pi{/}4$) and regular arrangement ($\theta = 0$) could be established, and it was verified by matching experimental data. Therefore, during the process of rotation, the inner relationship between angle θ and transmittance could be studied by introducing alignment factor.
2.3 Electric field induced regular arrangement and its proof
By imitating the definition of alignment factor [48] and combining with Malus’ Law, the alignment factor $A({\tau} )= \textrm{AVG}({{{\cos }^2}}\theta )= \frac{{I + 1.333}}{{4.667}}$ is proposed as shown in Fig. 5(a), it shows its relationships with I, normalized intensity and θ, angle between E and long axis of BPNS. It is consistent with facts stated before that BPNS which are regular arranged along E has larger normalized intensity. It means that the arrangement of flakes inside dispersion could be observed through polarized transmittance.
Fig. 5. a) Definition of alignment factor A(τ) and its relationship with normalized intensity (I) and the angle (θ) between long axis of BPNS and electric field; b) Macroscopic photos of electric-filed-induced birefringence with thermal convection inside dispersion.
To prove the thermal effect is the main mechanism of reducing, the polarized transmittance photos were shot. As macroscopic electric field induced birefringence photos of 1.333 mg/mL BPNS under E = 30 V/mm shown in Fig. 5(b). Thereinto, the red square represents the place where laser shot at, which is also the point of measuring transmittance, and the weak variation of transmittance could be observed inside red square, that it was increased then decreased after applying E, which is caused by thermal convection as marked. To measure it more precisely and further quantificational analyze it, alignment factors are calculated through normalized intensity according to relationship proposed in Fig. 5(a), and temperature variation are measured. Thereinto, the alignment factor $A({\tau} )$ in the ‘reduce’ section of unsteady state is fitted as shown in Fig. 6(a), whose relationship is $A(\tau )= \frac{{1.069}}{{t - 35}} + 0.594$, with increasing of time, the alignment factor $A({\tau} )$ is reduced efficiently, it is supposed to be caused by accumulation of heat, producing Joule heat increases the temperature inside dispersion and thermal emotion of BPNS, thus breaks regular arrangement and decreases the normalized intensity.
Fig. 6. a) Variations of A(τ) and b) temperature of 1.333 mg/mL under the only effect of electric field E = 30 V/mm.
To prove it, the temperature was measured at the middle of two electrodes, because the temperature is risen from two electrodes, then the measured temperature at the center could reflect the temperature variation inside dispersion, which could reflect the thermal convection efficiently. By fitting the temperature variation over time as shown in Fig. 6(b), which is caused by high electric field when the thermal effect of laser is low, considering the temperature is risen linearly, then the relationship was gotten as $Tem = 0.218\ast ({t - 35} )+ 298.210\; \textrm{K}$. Thus, the effect of thermal convection could be quantified as the formula, $A({\tau} )= \frac{{0.210}}{{Tem - 298.210}} + 0.595$, thereinto, Tem is the temperature at the point of measuring polarized transmittance. It proves that with increasing of temperature, the alignment factor got reduced. But the macroscopic electric field induced birefringence of graphene oxide is more obvious than BP, thus the light induced regular arrangement is proved by GO.
2.4 Light induced regular arrangement and its proof
The Wind-Chime model could be verified by the polarization-related cross optical switch system. The mechanisms have been discussed since the observation of Spatial Self-Phase Modulation (SSPM) in 2D material, one is that it is caused by the alignment of flakes, but it has not been verified yet. In 2011, the Wind-Chime model in SSPM was reported in Nano Lett. first time [49]. In 2015, PNAS reported the Wind-Chime model that the formation of SSPM pattern is caused by regular alignment of nanosheets and nonlocal ac electron coherence [15]. In 2020, Photonics Res. reported a general Wind-Chime model that not all the nanosheets are responsible for the formation [18]. To observe the regular alignment of nanosheets, the polarization-related cross optical switch system was designed, as shown in Fig. 6(a), by adding a pair of crossed polarized film in the direction vertical with SSPM, the arrangement of GONS in cuvette could be observed through the transmittance over orthogonal polarizers. Thus, the polarization-related cross optical switch system was built as shown in Fig. 6(b), thereinto, they are consisted by two orthogonal paths, one is shown in red, it is the focused 1300 nm laser to induce SSPM and detected by photodetector, another one is shown in yellow, it is the polarized light from LED, after passing through a pair of orthogonal PF (polarized film) 1 and PF 2, the polarized transmittance of dispersion could be observed directly through camera, and it reflect the different arrangement of flakes among different position inside dispersion.
The polarization-related cross optical switch uses an fs laser to induce SSPM and a weak polarization white light to observe it. Its mechanism and equipment setup is shown in Fig. 7(a,b) respectively. The SSPM is induced and its patterns are formatted by invisible laser with the wavelength at 1300 nm. Considering GONS as a 2D material with both significant electric field induced birefringence and SSPM, and their macroscopic electric field induced birefringence are more obvious than BPNS, they were chosen for the final proof. According to the theory of Wind-Chime model, when the SSPM are induced, dispersed 2D flakes, such as GONS, are arranged regularly along the vertical field, caused by their anisotropic structure and absorbance characters along different direction, the polarization direction of linear polarized light could be rotated according to the arrangement direction of GONS. Therefore, the Wind-Chime model could be verified by measuring the transmission of linear polarized light.
Fig. 7. a) Top view and b) equipment of the polarization-related cross optical switch system to observe Wind-Chime model in SSPM (PF: polarized film).
The Wind-Chime model in SSPM is verified by the rotation of linear polarized light. As shown in Fig. 8(a), according to the Wind-Chime model, the laser could create a vertical electric field to induce nonlocal ac electron coherence and regular arrangement of nanosheets, thus those regular arranged nanosheets could rotate the polarized light. The photodetector records the process of SSPM as shown in Fig. 8(b), which has similar phenomena with what reported before, and has four stages: i) focusing, ii) formation, iii) deformation and iv) final stage, which takes 1 s, 2 s and 11 s from focusing to occur respectively.
Fig. 8. a) Principle of observation Wind-Chime model in SSPM; b) different stages of SSPM in GONS dispersion: shooting laser: i) focusing, ii) formation, iii) deformation and removing laser: iv) final.
The polarized transmittance reflects the arrangement of flakes directly. By setting same experimental condition, polarized transmittance photos of dispersion are shot. At the moment that laser been shot to the red square area of sample, its polarized photo is shown in Fig. 9(a)-(i), with low transmittance inside cuvette. The polarized transmittance is remaining in an unbright level, by comparison, the transmittance near the inner wall is higher than the center. The dark region in the center is caused by the random arrangement of GONS inside dispersion as shown in Fig. 9(b)-(i). With the influence of inner wall, parts of GONS are arranged regularly near it, so the transmittance is higher near the inner wall. By setting the transmittance of brightest place in Fig. 9(a) as $A(\tau )= 1.00$, it could result an average alignment factor $A(\tau )= 0.52$ in Fig. 9(b)-(i).
Fig. 9. a) Transmission variation inside cuvette represents different rotation of linear polarized light; b) arrangement of GONS and their corresponding calculated average alignment factors after shooting laser at the place of red square.
After the laser are shot to dispersion, it breaks initial distribution of polarized light, as shown in ii-iv) of Fig. 9(a), the transmission begins to rise at the position of laser shot on, the original status of higher at the center but lower near the inner wall is broken. Its mechanism is shown in Fig. 9(b)-(ii), parts of GONS under the optical field begin to be arranged along the photo induced vertical electric field [15,18], resulting in the increasement of transmission, which has an average alignment factor $A(\tau )= 0.79$. And with continue shotting by laser, as shown in Fig. 9(a)-(iii.iv), the polarized transmittance are increased to a higher level, which has more flakes arranged regularly.
Caused by thermal heat effect of laser, some flakes are not regular arranged anymore. After the pattern at the upper part collapse to the center as shown in Fig. 8(b)-(iii), which is caused by the thermal convection [50]. In this article, they thought different temperature at the lower and upper part resulted in different density, then generated flow of liquid broke the regular arrangement of GONS. To prove it, as shown in Fig. 9(a)-(iv), a significant phenomenon is shown that transmission of laser point increases but reduces at upper part, and the area of low transmission rises. Then the arrangement of GONS is shown in Fig. 9(b)-(iv), by shooting laser, more GONS in the shooting range are arranged regularly, but GONS at the upper part becomes more irregular with thermal convection, thus it reduces the transmission at the upper part, resulting in $A(\tau )= 0.26$ at the upper part and $A(\tau )= 1$ at the lower part of laser shooting area. Then the reason of ‘deformation’ is confirmed to be the thermal convection.
The GONS return to random position after removing laser. As shown in Fig. 9(a)-(v), its transmission returns back to random position, at the influence of thermal convection (Q), flow induced force (Ff), rotational friction (f) and effect from Brownian motion (b) as shown in Fig. 9(b)-(v), GONS are rotated back to their random position, thus resulting in the recovery of transmission over two polarizers and $A(\tau )= 0.50$ back, which is close to initial alignment factor.
However, when reducing the laser intensity efficiently to the threshold of inducing SSPM, the variation of polarized transmission cannot be observed obviously. The reason was considered as that, there is no SSPM induced by laser, and the intensity of laser is weak that cannot create enough electric field to rotate and regular arrange flakes, then the variation of polarized transmittance cannot be observed.
3. Conclusion
In conclusion, we experimentally measured the polarized transmittance over 2D material dispersion, such as black phosphorus, which was caused by their regular arrangement. By setting rotation torque and establishing a modified model of flakes rotation, their dynamics were studied, it was proved by their fitting line of response time. Based on this model, by measuring the transmittance over a pair of orthogonal polarizers, electric field induced regular arrangement of nanosheets in dispersions were observed and discussed. By building polarization-related cross optical switch system, it was observed that there are partial regular arrangements of nanosheets when SSPM were induced. This result proved “Wind-Chime” model of regular arrangement in SSPM experimentally. This study adds new ways to explore the arrangement of nanosheets among different locations of dispersion, then the influences on it caused by series effects such as thermal convection could be researched.
Funding
National Natural Science Foundation of China (52227806); National Key Research and Development Program of China (2023YFC3906103).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
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